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.
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Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...
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A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a semiabelian ring R is π-regular if and only if N(R) is an ideal of R and R/N(R) is regular, which ex...
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ÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In ...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1959
ISSN: 0025-5645
DOI: 10.2969/jmsj/01130159