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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TL;DR: The main result in this article is that f ∈ L (R ) if and only if there exist an invertible matrix U ∈ T n (R) and an idempotence e ∈ R such that f(X)=U(eX+(1−e)X δ )U −1 for any X=(x ij )∈T n ( R ), where X δ =(x n+1−j n+ 1−i ).
16 citations
01 Oct 1963-Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
TL;DR: A graph-theoretic characterization of idempotent Boolean relation matrices of finite order and a formal results are exemplified in an investigation of the asymptotic forms of a recursive model of an information system which affords a conjoin t representation of processes of communication and derivation of information.
Abstract: This paper presents a graph-theoretic characterization of idempotent Boolean relation matrices of finite order. A relation-theoretic point of view is adopted in the paper. Idempotent matrices appear in the sequence of powers of any Boolean relation matrix, and are of purely theoretical as well as applied interest in connection with issues of convergence. The results provide a detailed description of the connectivity and cyclic structure of the directed graphs of idempotent matrices. The study is basically motivated by certain connectivity and flow problems which arise in the analysis of largescale information systems. The formal results are exemplified in an investigation of the asymptotic forms of a recursive model of an information system which affords a conjoin t representation of processes of communication and derivation of information. A second principal application is given in a process formulation for the generation of cons istent rank orderings. The relation between system des ign and idempotent forms is exhibited in the two applications.
16 citations
TL;DR: In this paper, the generalized inverses in a Banach algebra with respect to two idempotents p and q were investigated, and the obtained results extend and generalize some well-known results for matrices or operators.
Abstract: In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents p and q. Some new characterizations and explicit representations for these generalized inverses, such as a (2) p,q, a (1,2) p,q and a (2,l) p,q will be presented. The obtained results extend and generalize some well-known results for matrices or operators.
15 citations
TL;DR: It is shown that every semigroup pseudovarieties containing a group not in the subpseudovariety generated by all idempotent generated members of has no finite basis of pseudoidentities provided the five-element idem Potent generated 0-simple semigroup lies in .
Abstract: We show that every semigroup pseudovariety containing a group not in the subpseudovariety generated by all idempotent generated members of has no finite basis of pseudoidentities provided the five-element idempotent generated 0-simple semigroup lies in . This gives, in particular, a counterexample to a conjecture by J. Almeida.
15 citations
01 Jun 2007
TL;DR: In this paper, the authors give necessary and sufficient conditions for Sn−1 to be generated by idempotents over Euclidean domains and free left T -sets of finite rank, where T is a cancellative monoid in which every finitely generated left ideal is principal.
Abstract: If A is a stable basis algebra of rank n, then the set Sn−1 of endomorphisms of rank at most n − 1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn−1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T -sets of finite rank, where T is cancellative monoid in which every finitely generated left ideal is principal.
15 citations