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)
ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES

H. Hejazipour; A. R. Naghipour

Volume 9, Issue 2 , January 2022, , Pages 175-192

https://doi.org/10.22044/jas.2020.9745.1474

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 More

ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS

M. Rezagholibeigi; A. R. Naghipour

Volume 7, Issue 1 , September 2019, , Pages 51-68

https://doi.org/10.22044/jas.2018.6939.1340

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 More

THE ZERO-DIVISOR GRAPH OF A MODULE

A. Naghipour

Volume 4, Issue 2 , January 2017, , Pages 155-171

https://doi.org/10.22044/jas.2017.858

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 More

GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

A.R. Naghipour

Volume 3, Issue 1 , September 2015, , Pages 23-30

https://doi.org/10.22044/jas.2015.484

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 More

SOME RESULTS ON STRONGLY PRIME SUBMODULES

A.R. Naghipour

Volume 1, Issue 2 , January 2014, , Pages 79-89

https://doi.org/10.22044/jas.2014.228

Abstract
  Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. In this paper, we study more properties of strongly prime submodules. It is shown that a ...  Read More