En
  • دکتری (1368)

    ریاضی محض - جبر غیر جابجایی

    شفیلد، انگلستان

  • کارشناسی‌ارشد (1365)

    ریاضی محض

    شفیلد، انگلستان

  • کارشناسی (1358)

    ریاضی محض

    مدرسه عالی پارس، ایران

  • جبر ناجابجایی
  • حلقه های گروهی

    .لیسانس ریاضی محض، 1358 ، مدرسه عالی پارس .کارشناسی ارشد ریاضیات محض، 1365، دانشگاه شفیلد، انگلستان .دکتری ریاضیات محض، با درجه ممتاز، 1368، دانشگاه شفیلد عضو هیئت علمی گروه ریاضی محض، دانشکده علوم ریاضی، از سال 1368

    ارتباط

    رزومه

    Weakly principally quasi-Baer skew generalized power series rings

    Ali Majidinya, Ahmad Moussavi
    Journal PapersApplicable Algebra in Engineering, Communication and Computing , 2021 March 18, {Pages 17-Jan }

    Abstract

    Let be a strictly totally ordered monoid and R an-weakly rigid ring, where is a monoid homomorphism. In this paper, we study the weakly pq-Bear property of the skew generalized power series ring. As a consequence, the weakly pq-Baer property of the skew power series ring and the skew Laurent power series ring are determined, where is a ring endomorphism of R.

    Nil skew α-Armendariz amalgamated rings

    N Farshad, SA Safarisabet, A Moussavi
    Journal Papers , , {Pages }

    Abstract

    -BAER -RINGS

    A Shahidikia, HHS Javadi, A Moussavi
    Journal Papers , , {Pages }

    Abstract

    Some characterizations of 2-primal skew generalized power series rings

    Kamal Paykan, Ahmad Moussavi
    Journal PapersCommunications in Algebra , 2020 January 24, {Pages 12-Jan }

    Abstract

    A skew generalized power series ring R [[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal’cev-Neumann series rings, the “untwisted” versions of all of these, and generalized power series rings. In this paper we obtain necessary and sufficient conditions on R, S, and ω such that t

    A characterization of extending generalized triangular matrix rings

    Rasul Mohammadi, Ahmad Moussavi, Masoome Zahiri
    Journal PapersJournal of Algebra and Its Applications , 2020 January 8, {Pages 2150016 }

    Abstract

    A right module is extending if every submodule is essential in a direct summand of . In this note, we obtain a characterization of the right extending generalized triangular matrix rings. This answers a question which was raised in “E. Akalan, G. F. Birkenmeier and A. Tercan, Characterizations of extending modules and -extending generalized triangular matrix rings, Comm. Algebra 40 (2012) 1069–1085”.

    On quasi-Armendariz skew monoid rings

    Mohammad Habibi, Ahmad Moussavi, Raoufeh Manaviyat
    Journal PapersJournal of New Researches in Mathematics , 2020 May 4, {Pages }

    Abstract

    Let be a unitary ring with an endomorphism and be the free monoid generated by with added, and be a factor of setting certain monomial in to , enough so that, for some natural number , . In this paper, we give a sufficient condition for a ring such that the skew monoid ring is quasi-Armendariz (By Hirano a ring is called quasi-Armendariz if whenever and in satisfy , we have for every and ) and provide rich classes of non-semiprime quasi-Armendariz rings. Let be a unitary ring with an endomorphism and be the free monoid generated by with added, and be a factor of setting certain monomial in to , enough so that, for some natural number , . In this paper, we give a sufficient condition for a ring such that the skew m

    Generalized quasi-Baer -rings and Banach -algebras

    Morteza Ahmadi, Nasser Golestani, Ahmad Moussavi
    Journal PapersCommunications in Algebra , Volume 48 , Issue 5, 2020 May 3, {Pages 2207-2247 }

    Abstract

    We say that a -ring R is a generalized quasi-Baer -ring if for any ideal I of the right annihilator of is generated, as a right ideal, by a projection, for some positive integer n depending on I. A unital -ring R is left primary if and only if R is a generalized quasi-Baer -ring with no nontrivial central projections. We study basic properties of such rings and we prove their permanence properties such as the Morita invariance. We show that this notion is well-behaved with respect to polynomial extensions and certain triangular matrix extensions and group rings. A sheaf representation for such -rings is also proved. We obtain algebraic examples which are generalized quasi-Baer -rings but are not quasi-Baer -rings. We show that for pre-C*-

    Skew Inverse Laurent Series Extensions of Weakly Principally Quasi Baer Rings

    S Mehralinejadian, A Moussavi, S Sahebi
    Journal PapersJournal of Algebra and its Applications , 2020 June 17, {Pages }

    Abstract

    A ring R is called weakly principally quasi Baer or simply (weakly pq-Baer) if the right annihilator of a principal right ideal is right s-unital by right semicentral idempotents, which implies that R modulo the right annihilator of any principal right ideal is flat. We study the relationship between the weakly pq-Baer property of a ring R and those of the skew inverse series rings R ((x− 1; σ, δ)) and R [[x− 1; σ, δ]], for any automorphism σ and derivation δ of R. Examples to illustrate and delimit the theory are provided.

    Jordan Automorphism of Morita Context Algebras

    Ahmad Moussavi, Masoome Zahiri, Rasul Mohammadi
    Journal PapersBulletin of the Malaysian Mathematical Sciences Society , 2020 August 16, {Pages 14-Jan }

    Abstract

    The aim of this article is to determine entirely the Jordan automorphisms of generalized matrix rings of Morita contexts. Necessary and sufficient conditions are obtained for an -linear map on a general Morita context to be a Jordan homomorphism. Moreover, some conditions are studied, under which, any Jordan automorphism of a general Morita context is either an automorphism or an anti-automorphism.

    Rings whose singular ideals are nil

    M Ahmadi, A Moussavi
    Journal PapersCommunications in Algebra , Volume 48 , Issue 11, 2020 November 1, {Pages 4796-4808 }

    Abstract

    It is well known that when a ring R satisfies ACC on right annihilators of elements, then the right singular ideal of R is nil, in this case, we say R is right nil-singular. Many classes of rings whose singular ideals are nil, but do not satisfy the ACC on right annihilators, are presented and the behavior of them is investigated with respect to various constructions, in particular skew polynomial rings and triangular matrix rings. The class of right nil-singular rings contains π-regular rings and is closed under direct sums. Examples are provided to explain and delimit our results.

    Modules with annihilation property

    Rasul Mohammadi, Ahmad Moussavi, Masoome Zahiri
    Journal PapersJournal of Algebra and Its Applications , 2020 July 31, {Pages 2150126 }

    Abstract

    Let be an associative ring with identity. A right -module is said to have Property (), if each finitely generated ideal has a nonzero annihilator in . Evans [Zero divisors in Noetherian-like rings, Trans. Amer. Math. Soc. 155(2) (1971) 505–512.] proved that, over a commutative ring, zero-divisor modules have Property (). We study and construct various classes of modules with Property (). Following Anderson and Chun [McCoy modules and related modules over commutative rings, Comm. Algebra 45(6) (2017) 2593–2601.], we introduce -dual McCoy modules and show that, for every strictly totally ordered monoid , faithful symmetric modules are -dual McCoy. We then use this notion to give a characterization for modules with Property (). For a fa

    Modules in which the annihilator of a fully invariant submodule is pure

    P Amirzadeh Dana, A Moussavi
    Journal PapersCommunications in Algebra , Volume 48 , Issue 11, 2020 November 1, {Pages 4875-4888 }

    Abstract

    A ring R is called left AIP if R modulo the left annihilator of any ideal is flat. In this paper, we characterize a module MR for which the endomorphism ring is left AIP. We say a module MR is endo-AIP (resp. endo-APP) if M has the property that “the left annihilator in of every fully invariant submodule of M (resp. for every ) is pure as a left ideal in ”. The notion of endo-AIP (resp. endo-APP) modules generalizes the notion of Rickart and p.q.-Baer modules to a much larger class of modules. It is shown that every direct summand of an endo-AIP (resp.endo-APP) module inherits the property and that every projective module over a left AIP (resp. APP)-ring is an endo-AIP (resp. endo-APP) module.

    Generalized -Baer rings

    Ali Shahidikia, Hamid Haj Seyyed Javadi, Ahmad Moussavi
    Journal PapersTurkish Journal of Mathematics , Volume 44 , Issue 6, 2020 November 17, {Pages 2021-2040 }

    Abstract

    We call a ring generalized right -Baer, if for any projection invariant left ideal of , the right annihilator of is generated, as a right ideal, by an idempotent, for some positive integer , depending on . In this paper, we investigate connections between the\g -Baer rings and related classes of rings (eg, -Baer, generalized Baer, generalized quasi-Baer, etc.) In fact, generalized right -Baer rings are special cases of generalized right quasi-Baer rings and also are a generalization of -Baer and generalized right Baer rings. The behavior of the generalized right -Baer condition is investigated with respect to various constructions and extensions. For example, the trivial extension of the generalized right -Baer ring and the full matrix r

    Triangular matrix rings of selfinjective rings

    M Zahiri, A Moussavi, R Mohammadi
    Journal PapersCommunications in Algebra , 2020 November 17, {Pages 07-Jan }

    Abstract

    A module M is said to be generalized extending if for every submodule there exists a direct summand D of M containing N such that D/N is a singular module. In this note we prove that a ring R is right self-injective if and only if the triangular ring is right generalized extending. This answers a question which was raised in A. Akalan, G.F. Birkenmeier, A. Tercan, Characterizations of extending modules and -extending generalized triangular matrix rings, Commun. Algebra 40 (2012), 1069–1085.

    Involutive triangular matrix algebras

    Morteza Ahmadi, Ahmad Moussavi
    Journal PapersHacettepe Journal of Mathematics and Statistics , 2020 January 1, {Pages 06-Jan }

    Abstract

    In this paper, we provide new examples of Banach∗-subalgebras of the matrix algebra M n (A). For any involutive algebra, we define two involutions on the triangular matrix extensions. We prove that the triangular matrix algebras over any commutative unital C∗-algebra, are Banach∗-algebras and that the primitive ideals of these algebras and some of their Banach∗-subalgebras are all maximal.

    Generalized Baer rings

    Ahmad MOUSSAVI, Hamid Haj Seyyed Javadi, Ali Shahidikia
    Journal PapersTurkish Journal of Mathematics , Volume 1 , Issue 1, 2020 December 5, {Pages }

    Abstract

    Abstract: We call a ring R generalized right π-Baer, if for any projection invariant left ideal Y of R, the right annihilator of Y n is generated, as a right ideal, by an idempotent, for some positive integer n, depending on Y. In this paper, we investigate connections between the generalized π-Baer rings and related classes of rings (eg, π-Baer, generalized Baer, generalized quasi-Baer, etc.) In fact, generalized right π-Baer rings are special cases of generalized right quasi-Baer rings and also are a generalization of π-Baer and generalized right Baer rings. The behavior of the generalized right π-Baer condition is investigated with respect to various constructions and extensions. For example, the trivial extension of a generalized

    On a skew McCoy ring

    Masoome Zahiri, Ahmad Moussavi, Rasul Mohammadi
    Journal PapersCommunications in Algebra , Volume 47 , Issue 10, 2019 October 3, {Pages 4061-4065 }

    Abstract

    A ring R with an endomorphism σ is called σ-skew McCoy, if for any zero-divisor f(x) in the skew polynomial ring R[x; σ], there exists a nonzero element with f(x)c = 0. In this note, we show that there exists a ring R and an endomorphism σ such that the matrix ring M2(R) is σ-skew McCoy. This gives a negative answer to the question posed in “A. R. Nasr-Isfahani, On semiprime right Goldie McCoy rings, Commun. Algebra 42 (2014) 1565-1570”.

    Associated primes and primary right ideals of generalized triangular matrix rings

    M Zahiri, A Moussavi, R Mohammadi
    Journal PapersCommunications in Algebra , 2019 January 16, {Pages 14-Jan }

    Abstract

    Let SMR be an (S, R)-bimodule of the rings R and S. We determine the associated primes of a formal triangular matrix ring T=(R 0 MS). Indeed, we show that A ss (TT)={(A ss ((R⊕ M) R) 0 MS)}∪{(R 0 MA ss (l S (M)))}. We then obtain necessary and sufficient conditions for the tertiary decomposition theory to exist on a module over an arbitrary ring. Consequently, we classify all the tertiary right ideals of the formal triangular matrix rings.

    ARCHIMEDEAN SKEW GENERALIZED POWER SERIES RINGS

    Ahmad Moussavi, Farzad Padashnik, Kamal Paykan
    Journal PapersCommunications of the Korean Mathematical Society , Volume 34 , Issue 2, 2019 January , {Pages 361-374 }

    Abstract

    Let R be a ring,() a strictly ordered monoid, and a monoid homomorphism. In [18], Mazurek, and Ziembowski investigated when the skew generalized power series ring is a domain satisfying the ascending chain condition on principal left (resp. right) ideals. Following [18], we obtain necessary and sufficient conditions on R, S and such that the skew generalized power series ring is a right or left Archimedean domain. As particular cases of our general results we obtain new theorems on the ring of arithmetical functions and the ring of generalized power series. Our results extend and unify many existing results.

    Polynomial extensions of modules with the quasi-Baer property

    P Amirzadeh Dana, A Moussavi
    Journal PapersJournal of Algebra , 2019 October 11, {Pages }

    Abstract

    In this paper it is shown that, for a module M over a ring R with S= E n d R (M), the endomorphism ring of the R [x]-module M [x] is isomorphic to a subring of S [[x]]. Also the endomorphism ring of the R [[x]]-module M [[x]] is isomorphic to S [[x]]. As a consequence, we show that for a module M R and an arbitrary nonempty set of not necessarily commuting indeterminates X, M R is quasi-Baer if and only if M [X] R [X] is quasi-Baer if and only if M [[X]] R [[X]] is quasi-Baer if and only if M [x] R [x] is quasi-Baer if and only if M [[x]] R [[x]] is quasi-Baer. Moreover, A module M R with IFP, is Baer if and only if M [x] R [x] is Baer if and only if M [[x]] R [[x]] is Baer. It is also shown that, when M R is a finitely generated module, an

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    دروس نیمسال جاری

    • دكتري
      حلقه هاي گروهي ( واحد)
      دانشکده علوم ریاضی، گروه رياضي محض
    • كارشناسي ارشد
      نظريه حلقه و مدول ( واحد)

    دروس نیمسال قبل

    • كارشناسي ارشد
      جبر پيشرفته ( واحد)
      دانشکده علوم ریاضی، گروه رياضي محض
    • دكتري
      جبر ناجابجائي (1) ( واحد)
    • 1399
      عبدي, فاطمه
      وارون هاي تعميم يافته در حلقه ها
    • 1397
      ارميده, نسيبه
      حلقه هاي از نوع cp-بئر
    • 1397
      مالكي, ياسر
    • 1398
      حاج علي اكبري, ازاده
    • 1398
      دودونگه, ابراهيم
    • عضو نشریه AMS
    • عضو شورای علمی گروه ریاضی و انفورماتیک جهاد دانشگاهی تربیت مدرس
      داده ای یافت نشد

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