Zero Divisor Graph for the Ring of Eisenstein Integers Modulo n

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

THE ZERO-DIVISOR GRAPH OF A MODULE

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 Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show tha...

متن کامل

On the Zero-divisor Cayley Graph of a Finite Commutative Ring

Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding co...

متن کامل

Properties of extended ideal based zero divisor graph of a commutative ring

This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.

متن کامل

On zero divisor graph of unique product monoid rings over Noetherian reversible ring

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

متن کامل

The Zero-Divisor Graph of a Commutative Ring

Ž . Ž . Let R be a commutative ring with 1 and let Z R be its set of Ž . Ž . zero-divisors. We associate a simple graph G R to R with vertices Ž . Ž . 4 Z R * s Z R y 0 , the set of nonzero zero-divisors of R, and for disŽ . tinct x, y g Z R *, the vertices x and y are adjacent if and only if xy s 0. Ž . Thus G R is the empty graph if and only if R is an integral domain. The main object of this...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Algebra

سال: 2014

ISSN: 2314-4106,2314-4114

DOI: 10.1155/2014/146873