Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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7 citations
Journal Article•
TL;DR: In this paper, it was shown that a semiring R is k-regular if and only if R is an additively idempotent semiring with identity, and if R n×n is K-regular.
Abstract: Generalizing the notion of regular ring in the sense of Von Neumann, Bourne, Adhikari, Sen and Wienert introduced the notion of k-regular semiring. In this paper, we investigate Q-ideals of the semiring of non-negative integers for which the quotient semiring is a semifield and a k-regular semiring. Also we prove that a semiring R is k-regular if and only if the quotient semiring R/I is k-regular for every Q-ideal I of R. Finally we prove that if R is an additively idempotent semiring with identity, then R is k-regular if and only if the matrix semiring R n×n is k-regular.
7 citations
6 citations
TL;DR: In this paper, it was proved that if A is a nonassociative algebra that verifies A 2 = A and has an idempotent, then A and its duplicate have isomorphic automorphism groups and isomorphic derivation algebras.
6 citations
01 Jan 2007
TL;DR: In this paper, the authors characterized the bijective linear preservers of idempotence on Tn(F) and the strong linear presers of idemepotence over Tn (F) are characterized.
Abstract: Let F be any field and let Tn(F) be the n × n upper triangular matrix space over F. We denote the set of all n × n upper triangular idempotent matrices over F by Pn(F). A map ϕ on Tn(F) is called a preserver of idempotence if ϕ(Pn(F)) ⊂ Pn(F); and a strong preserver of idempotence if ϕ(Pn(F)) = Pn(F). In this paper, we characterize the bijective linear preservers of idempotence on Tn(F). Further, the strong linear preservers of idempotence on Tn(F) are characterized. Mathematics Subject Classifications: 15A04; 15A03
6 citations