منابع مشابه
Zero Square Rings
A ring R for which x = 0 for all x e R is called a zerosquare ring. Zero-square rings are easily seen to be locally nilpotent. This leads to two problems: (1) constructing finitely generated zero-square rings with large index of nilpotence, and (2) investigating the structure of finitely generated zerosquare rings with given index of nilpotence. For the first problem we construct a class of zer...
متن کاملZero-sum Square Matrices
Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...
متن کاملSubrings of zero-dimensional rings
When Sarah Glaz, Bill Heinzer and the junior author of this article approached Robert with the idea of editing a book dedicated to his work, we asked him to give us a list of his work and to comment on it to the extent he felt comfortable. As usual, he was extremely thorough in his response. When the authors of this article began to consider what topic we wanted to write about, we were impresse...
متن کاملOn quasi-zero divisor graphs of non-commutative rings
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...
متن کاملZero-Divisor Graph of Triangular Matrix Rings over Commutative Rings
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; ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1969
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1969.30.811