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On Generalized Regular Local Ring
Science Journal of University of Zakho, 2015 A ring R is called a generalized Von Neumann regular local ring (GVNL-ring) if for any a∈R, either a or (1-a) is π-regular element. In this paper, we give some characterization and properties of generalized regular local rings.
Zubayda M. Ibraheem, Naeema A. Shereef
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On G-Regular Local Rings [PDF]
Communications in Algebra, 2008 In this article, we define a G-regular local ring as a commutative, noetherian, local ring, over which all totally reflexive modules are free. We study G-regular local rings and observe that they behave similarly to regular local rings. We extend Eisenbud's matrix factorization theorem and Knorrer's periodicity theorem to G-regular local rings.
Ryo Takahashi
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r-CLEAN RINGS RELATIVE TO RIGHT IDEALS [PDF]
Journal of Algebraic Systems, 2023 .An associative ring R with identity is called r¡clean ring if everyelement of R is the sum of a regular and an idempotent element. In this paper,we introduce the concept of r-clean rings relative to right ideal. We studyvarious properties of these rings.
H. Hakmi, B. Alussein
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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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FILTER REGULAR SEQUENCES AND LOCAL COHOMOLOGY MODULES [PDF]
Journal of Algebraic Systems, 2020 Let R be a commutative Noetherian ring. In this paper we consider some relations between filter regular sequence,regular sequence and system of parameters over R-modules.
J. Azami
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Stable range conditions for abelian and duo rings
Математичні Студії, 2022 The article deals with the following question: when does the classical ring of quotients of a duo ring exist and idempotents in the classical ring of quotients $Q_{Cl} (R)$ are there idempotents in $R$?
A. A. Dmytruk +2 more
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2014 A ring R is called local ring if it has exactly one maximal ideal. In this paper, we introduce some characterization and basic properties of this ring. Also, we studied the relation between local rings and Von Neumann regular rings and strongly regular ...
Zubayda Ibraheem, Anees Fthee
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2019 An ideal K of a ring R is called right (left) generalized pure (GP -ideal) if for every a ∈ K, there exists m ∈ Z+, and b ∈ K such that am = am b ( am = b am) . A ring R is called MLGP-ring if every right maximal ideal is left GP-ideal.
Raida mahmood, Ebtehal Mageed
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Central Localizations of Regular Rings [PDF]
Proceedings of the American Mathematical Society, 1974 In this paper we show that a ring R R is von Neumann regular (or a
Armendariz, E. P. +2 more
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Grothendieck–Serre in the quasi-split unramified case
Forum of Mathematics, Pi, 2022 The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified.
Kęstutis Česnavičius
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