Results 1 to 10 of about 17,431 (137)
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
doaj +2 more sources
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
exaly +2 more sources
UNIQUE FACTORIZATION IN REGULAR LOCAL RINGS [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1959 M Auslander, Auslander Maurice
exaly +4 more sources
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
doaj +1 more source
Local log-regular rings vs. toric rings
Communications in AlgebraLocal log-regular rings are a certain class of Cohen-Macaulay local rings that are treated in logarithmic geometry. Our paper aims to provide purely commutative ring theoretic proof of some ring-theoretic properties of local log-regular rings such as an explicit description of a canonical module, and the finite generation of the divisor class group.
exaly +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Regular Parameter Elements and Regular Local Hyperrings
Mathematics, 2021 Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring.
Hashem Bordbar, Irina Cristea
doaj +1 more source
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
openaire +2 more sources