Results 41 to 50 of about 708,128 (192)

ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS [PDF]

Journal of Algebraic Systems, 2019
Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$
M. Rezagholibeigi, A. R. Naghipour
doaj   +1 more source

Artinian Local Cohomology Modules

, 2007
Let R be a commutative Noetherian ring, α an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module is finitely generated for all i < t, then is finitely generated.
Siamak Yassemi, Keivan Borna Lorestani, Parviz Sahandi   +2 more
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CHARACTERIZATION THEOREMS OF S-ARTINIAN MODULES

, 2021
A module X over a commutative ring A is called S-Artinian, where S is a given multiplicatively closed subset of A, if every descending chain of sub-modules of X is S-stationary.
Unsal Tekir, Kar Ping Shum, OsamaA. Naji, Mehmet Özen   +3 more
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On the Genus of the Co-Annihilating Graph of Commutative Rings

Discussiones Mathematicae - General Algebra and Applications, 2019
Let R be a commutative ring with identity and 𝒰R be the set of all nonzero non-units of R. The co-annihilating graph of R, denoted by 𝒞𝒜R, is a graph with vertex set 𝒰R and two vertices x and y are adjacent whenever ann(x) ∩ ann(y) = (0).
Selvakumar K., Karthik S.
doaj   +1 more source

Artinian ideals in Noetherian rings

, 1975
We show that in a right and left Noetherian ring two-sided ideals which are Artinian as left submodules are also Artinian as right submodules.
T. H. Lenagan
core   +1 more source

A Note on Artinianess of Certain Generalized [PDF]

Journal of Sciences, Islamic Republic of Iran, 2008
Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-
doaj  

Embedding differential and skew polynomial rings into Artinian rings

, 1990
Under suitable hypotheses it is shown that a differential or skew polynomial ring can be embedded in an Artinian ring provided that its coefficient ring can be embedded in an Artinian ring.
William D. Blair, Lance W. Small
core   +1 more source

Neutrosophic Ideals in Artinian Rings and Their Application to AI-Driven Uncertainty Classification

Journal of Mathematics
This work examines the behaviour of neutrosophic ideals within the framework of Artinian rings. A key finding shows that a ring with unity is left (or right) Artinian if and only if every neutrosophic left (or right) ideal takes only finitely many ...
Amr Elrawy, Mohammed A. Saleem, Ali Yahya Hummdi, Ayat A. Temraz   +3 more
doaj   +1 more source

A typical graph structure of a ring [PDF]

Transactions on Combinatorics, 2015
The zero-divisor graph of a commutative ring R with respect to nilpotent elements is a simple undirected graph $Gamma_N^*(R)$ with vertex set Z_N(R)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where Z_N(R)={x
R. Kala , S. Kavitha
doaj  

고정환의 Semisimple Artinian 환

, 1984
G가 R위에 작용하는 automorphism군일 때 G가 고정시키는 R의 모든 원의 집합을 RG라 하면 RG가 semisimple Artinian 일 때 R도 semisimple Artinain이다.Let G be a finite group of automorphisms of the ring R, and RG be the ring of fixed points of G in R.
Lee,Tong-su
core   +1 more source