نتایج جستجو برای: zero divisor graph ideal
تعداد نتایج: 424665 فیلتر نتایج به سال:
Let R be a noncommutative ring. The zero-divisor graph of R, denoted by Γ(R), is the (directed) graph with vertices Z(R)∗ = Z(R)− {0}, the set of nonzero zero-divisors of R, and for distinct x, y ∈ Z(R)∗, there is an edge x → y if and only if xy = 0. In this paper we investigate the zero-divisor graph of triangular matrix rings over commutative rings. Mathematics Subject Classification: 16S70; ...
We recall several results of zero divisor graphs of commutative rings. We then examine the preservation of the diameter of the zero divisor graph of polynomial and power series rings.
Let R be a commutative ring with unity. The set Z(R) of zero-divisors in a ring does not possess any obvious algebraic structure; consequently, the study of this set has often involved techniques and ideas from outside algebra. Several recent attempts, among them [2], [3] have focused on studying the so-called zero-divisor graph ΓR, whose vertices are the zero-divisors of R, with xy being an ed...
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 in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...
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