منابع مشابه
Commuting $pi$-regular rings
R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.
متن کاملcommuting $pi$-regular rings
r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.
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We prove that the commuting probability of a finite ring is no larger than the commuting probabilities of its subrings and quotients, and characterize when equality occurs in such a comparison.
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We study periodic rings that are finitely generated as groups. We prove several structure results. We classify periodic rings that are free of rank at most 2, and also periodic rings R such that R is finitely generated as a group and R/t(R) Z. In this way, we construct new classes of periodic rings. We also ask a question concerning the connection to periodic rings that are finitely generated a...
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Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with a vertex set $Rsetminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if $ab=ba$. In this paper, we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$. It is shown that, $Gamma(R)$ is the disjoint ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1984
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171284000417