Volume 11 (2023-2024)
Volume 10 (2022-2023)
Volume 9 (2021-2022)
Volume 8 (2020-2021)
Volume 7 (2019-2020)
Volume 6 (2018-2019)
Volume 5 (2017-2018)
Volume 4 (2016-2017)
Volume 3 (2015-2016)
Volume 2 (2014-2015)
Volume 1 (2013-2014)
Author = A.R. Naghipour
Number of Articles: 5
ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES
Volume 9, Issue 2 , January 2022, , Pages 175-192
Abstract
Let $M(X, \mathcal{A}, \mu)$ be the ring of real-valued measurable functionson a measurable space $(X, \mathcal{A})$ with measure $\mu$.In this paper, we study the zero-divisor graph of $M(X, \mathcal{A}, \mu)$,denoted by $\Gamma(M(X, \mathcal{A}, \mu))$.We give the relationships among graph properties ... Read MoreON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS
Volume 7, Issue 1 , September 2019, , Pages 51-68
Abstract
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 $x+uyv$ is a unit of $R$. In this paper, basic properties ... Read MoreTHE ZERO-DIVISOR GRAPH OF A MODULE
Volume 4, Issue 2 , January 2017, , Pages 155-171
Abstract
Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for ... Read MoreGENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
Volume 3, Issue 1 , September 2015, , Pages 23-30
Abstract
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem ... Read MoreSOME RESULTS ON STRONGLY PRIME SUBMODULES
Volume 1, Issue 2 , January 2014, , Pages 79-89