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 article, it was proved that the variety of representable idempotent commutative residuated lattices is locally finite and the n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each.
Abstract: It is proved that the variety of representable idempotent commutative residuated lattices is locally finite The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each A constructive characterization of the subdirectly irreducible algebras is provided, with some applications The main result implies that every finitely based extension of positive relevance logic containing the mingle and Godel-Dummett axioms has a solvable deducibility problem
35 citations
TL;DR: In this article, it was shown that if a finite algebra generates a congruence distributive variety, then the subalgebras of the powers of satisfy a certain kind of intersection property.
Abstract: We prove that if a finite algebra generates a congruence distributive variety, then the subalgebras of the powers of satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.
35 citations
TL;DR: In this paper, the authors proposed a semigroup with the additional relation of an additional relation between the semigroup's members and the associated relations, which is called aband or anidempotent semigroup.
Abstract: Let B be a semigroup with the additional relation
$$\begin{gathered} xx \Rightarrow x \hfill \\ xyz \Rightarrow xz if x \mathop {CI}\limits_ = z and xy\mathop {CI}\limits_ = z \hfill \\ \end{gathered} $$
B is called aband or anidempotent semigroup [3].
34 citations
TL;DR: In this article, the Jacobson radical of a Jordan algebra has been defined as the maximal ideal consisting entirely of quasi-invertible elements, in analogy with the case of associative algebras.
34 citations
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TL;DR: In this article, the maximal subgroups of the free idempotent generated semigroup on a biordered set were studied and shown to be isomorphic to the free abelian group of rank 2.
Abstract: We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free abelian group of rank 2. This is the first example of a non-free subgroup of a free idempotent generated semigroup.
34 citations