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: In this paper, it was shown that the groups associated to idempotent elements of S(R) are extensions of class groups of overrings of (R) by means of direct products of archimedean groups of localizations of R at idempotsent prime ideals.
Abstract: The class semigroup of a commutative integral domain R is the semigroup S(R) of the isomorphism classes of the nonzero ideals of R with operation induced by multiplication. We consider Prufer domains of finite character, i.e. Prufer domains in which every nonzero ideal is contained but in a finite number of maximal ideals. In [1] it is proved that, if R is such a Prufer domain, then the semigroup S(Ris a Clifford semigroup, namely it is the disjoint union of the subgroups associated to each idempotent element. In [2] we gave a description of a generating set for the A-semilattice of the idempotent elements of S(R). In this paper we consider the constituent groups of the class semigroup. We prove that the groups associated to idempotent elements of S(R) are extensions of class groups of overrings of (R) by means of direct products of archimedean groups of localizations of(R) at idempotent prime ideals.
31 citations
TL;DR: In this paper, the DMP inverse is extended from matrices to operators and many closely equivalent relations among these inverses are investigated by using appropriate idempotents, and some new properties of the inverse are obtained and some known results are generalized.
Abstract: Let $$\mathcal {H}$$H be a Hilbert space The recently introduced notions of the DMP inverse are extended from matrices to operators The group, Moore---Penrose, Drazin inverses are integrated by DMP inverse and many closely equivalent relations among these inverses are investigated by using appropriate idempotents Some new properties of DMP inverse are obtained and some known results are generalized
31 citations
TL;DR: It is shown that the factor weighted automaton with respect to the greatest forward bisimulation equivalence matrix on aweighted automaton A is the unique (upto an isomorphism)minimal automaton in the class of all weighted automata which are forward bisIMulation equivalent to A.
31 citations
TL;DR: In this paper, the problem of characterizing linear operators on the matrices over a semiring such that a linear operator is idempotent if and only if it is a function of the semiring is considered.
31 citations
TL;DR: In this paper, a simple example is given to illustrate that an idempotent state may not be the Haar state of any subgroup in the case of compact quantum groups.
Abstract: A simple example is given to illustrate that an idempotent state may not be the Haar state of any subgroup in the case of compact quantum groups.
31 citations