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, an introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.
Abstract: An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones. Such results include characterizations of simplicity, characterizations of the exchange property, and cancellation conditions for the K-theoretic monoid of equivalence classes of idempotent matrices.
90 citations
TL;DR: A general theory for abundant semigroups is developed in this article, where a semigroup S in this class is defined as a set of idempotents and the subsemigroup of S generated by E is given.
Abstract: A general theory for a class of abundant semigroups is developed. For a semigroup S in this class let E be its set of idempotents and the subsemigroup of S generated by E. When is regular there is a homomorphism with a number of desirable properties from S onto a full subsemigroup of the Hall semigroup T . From this fact, analogues of results in the regular case are obtained for *-simple and ℐ*-simple abundant semigroups.
87 citations
TL;DR: In this paper, a semilattice is defined as an algebra with one binary operation ∧, which is associative, commutative, and idempotent.
Abstract: A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relation defines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.
86 citations
TL;DR: Normalized rewriting is introduced, a new rewrite relation which generalizes former notions of rewriting modulo a set of equations E , dropping some conditions on E , and gives a new completion algorithm for normalized rewriting.
85 citations
84 citations