Results 31 to 40 of about 600,300 (198)
On minimal artinian modules and minimal artinian linear groups
International Journal of Mathematics and Mathematical Sciences, 2001 The paper is devoted to the study of some important types of minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and FC‐groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups.
Leonid A. Kurdachenko, Igor Ya. Subbotin
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δ-Small Submodules and δ-Supplemented Modules
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an ...
Yongduo Wang
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 In this paper we provide various properties of Rad-⊕-supplemented modules. In particular, we prove that a projective module M is Rad- ⊕-supplemented if and only if M is ⊕-supplemented, and then we show that a commutative ring R is an artinian serial ring
Türkmen Ergül
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A characterization of locally artinian modules
Journal of Algebra, 1990 The starting point for this paper is a well known theorem of Osofsky, namely that a ring R is semiprime Artinian if and only if every cyclic right R-module is injective. At the heart of Osofsky's proof is the observation: if R is a right self-injective von Neumann regular ring and \(\{e_ i:\) \(i\in I\}\) an infinite family of orthogonal idempotents ...
van Huynh, Dinh, Wisbauer, Robert
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The Artinian Berger Conjecture [PDF]
, 2021 We propose an Artinian version of Berger's Conjecture for curves, concerning the module of K\"ahler differentials of an algebra. Our version implies Berger's Conjecture in characteristic 0. We establish our Artinian Berger Conjecture in a number of cases,
Cortiñas, Guillermo Horacio +2 more
core
On the structure of some minimax-antifinitary modules
Karpatsʹkì Matematičnì Publìkacìï, 2015 Let $R$ be a ring and $G$ a group. An $R$-module $A$ is said to be {\it minimax} if $A$ includes a noetherian submodule $B$ such that $A/B$ is artinian.
V.A. Chupordia
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Tạp chí Khoa học, 2023 In this paper, we introduce condition (∗) for modules and show that every CS-semisimple ring having condition (∗) is a QF ring.
Le Van An, Nguyen Thi Hai Anh
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Subrings of I-rings and S-rings
International Journal of Mathematics and Mathematical Sciences, 1997 Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
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On Cohen's theorem for Artinian modules [PDF]
, 2022 In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with $(0:_RM)\subseteq \mathfrak{p}$, there exists a submodule $N^\mathfrak{p}$ of $M$ such that $M/N^\mathfrak{p}$ is ...
Zhang, Xiaolei, Kim, Hwankoo, Qi, Wei
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Journal of Mathematics, 2023 Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A ...
Zhanmin Zhu
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