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.
Papers published on a yearly basis
Papers
More filters
01 Mar 2018
TL;DR: It is shown that if an idempotent semiring is equipped with an involution which satisfies certain conditions, then it can be organized into a residuated lattice satisfying the double negation law.
Abstract: Every residuated lattice can be considered as an idempotent semiring. Conversely, if an idempotent semiring is finite, then it can be organized into a residuated lattice. Unfortunately, this does not hold in general. We show that if an idempotent semiring is equipped with an involution which satisfies certain conditions, then it can be organized into a residuated lattice satisfying the double negation law. Also conversely, every residuated lattice satisfying the double negation law can be considered as an idempotent semiring with an involution satisfying the mentioned conditions.
7 citations
TL;DR: In this article, conditions on the scalars defining a plenary train algebra of rank 4 were studied to assure the existence of such an idempotent element, which is an open problem to be solved.
Abstract: The existence of idempotent elements in plenary train algebras of rank greater than 3, is an open problem to be solved. J. Carlos Gutierrez's results on plenary train algebras in Gutierrez (2000) are based on the underlying assumption of the existence of an idempotent. In this article we study conditions on the scalars defining a plenary train algebra of rank 4 to assure the existence of such an idempotent.
7 citations
TL;DR: In this article, it was shown that every proper closed ideal of a Banach algebra with a bounded approximate identity (BAI) is contained in a proper closed Banach ideal with a BAI and that a multiplier T:A → A has a closed range iff T factors as a product of an idempotent multiplier and an invertible multiplier.
Abstract: In this paper we prove the Theorem: Let A be a Banach algebra with a bounded approximate identity (=BAI) such that every proper closed ideal of A is contained in a proper closed ideal with a BAI. Then a multiplier T:A → A has a closed range iff T factors as a product of an idempotent multiplier and an invertible multiplier.
7 citations
TL;DR: This work reports on progress in characterizing K -valued FCA in algebraic terms, and states the importance of FCA-related concepts for dual order homomorphisms of linear spaces over idempotent semifields, specially congruences, the lattices of extents, intents and formal concepts.
7 citations
TL;DR: This article shows that there exists an anti-unification problem with a single idempotent symbol that has an infinite minimal complete set of generalizations, and develops an algorithm that takes an arbitrary idempotsent anti- unification problem and computes a representation of its solution set in the form of a regular tree grammar.
Abstract: In this article, we address two problems related to idempotent anti-unification. First, we show that there exists an anti-unification problem with a single idempotent symbol that has an infinite minimal complete set of generalizations. It means that anti-unification with a single idempotent symbol has infinitary or nullary generalization type, similar to anti-unification with two idempotent symbols, shown earlier by Loic Pottier. Next, we develop an algorithm that takes an arbitrary idempotent anti-unification problem and computes a representation of its solution set in the form of a regular tree grammar. The algorithm does not depend on the number of idempotent function symbols in the input terms. The language generated by the grammar is the minimal complete set of generalizations of the given anti-unification problem, which implies that idempotent anti-unification is infinitary.
7 citations