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- W1576494829 abstract "A ring R is called a ( von Neumann ) regular ring if for every $ x in R$; x= xyx for some $ y in R$ . It is well-known that for any ring R and any positive integer n , the full matrix ring $ M_n ( R )$ is regular if and only if R is a regular ring. This paper examines this property on any additively commutative semiring S with zero. The regularity of S is defined analogously. We show that for a positive integer n, if $ M _n( S )$ is a regular semiring, then S is a regular semiring but the converse need not be true for n = 2. And for n 3, $ M _n( S )$ is a regular semiring if and only if S is a regular ring." @default.
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- W1576494829 date "2012-03-28" @default.
- W1576494829 modified "2023-09-23" @default.
- W1576494829 title "On Regular Matrix Semirings" @default.
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