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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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Book ChapterDOI
Peter Jipsen1
15 May 2017
TL;DR: A finitely-based variety of cyclic involutive GBI-algebras are constructed from so-called weakening relations, and it is proved that the class of weakening relation algebrAs is not finitely axiomatizable.
Abstract: This paper investigates connections between algebraic structures that are common in theoretical computer science and algebraic logic. Idempotent semirings are the basis of Kleene algebras, relation algebras, residuated lattices and bunched implication algebras. Extending a result of Chajda and Langer, we show that involutive residuated lattices are determined by a pair of dually isomorphic idempotent semirings on the same set, and this result also applies to relation algebras. Generalized bunched implication algebras (GBI-algebras for short) are residuated lattices expanded with a Heyting implication. We construct bounded cyclic involutive GBI-algebras from so-called weakening relations, and prove that the class of weakening relation algebras is not finitely axiomatizable. These algebras play a role similar to representable relation algebras, and we identify a finitely-based variety of cyclic involutive GBI-algebras that includes all weakening relation algebras. We also show that algebras of down-closed sets of partially-ordered groupoids are bounded cyclic involutive GBI-algebras.

17 citations

Posted Content
TL;DR: In this article, it was shown that Brauer graph algebras coincide with the class of indecomposable idempotent biserial weighted surface algesbras.
Abstract: We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated to triangulated surfaces with arbitrarily oriented triangles, investigated in [17] and [18]. Moreover we prove that Brauer graph algebras are idempotent algebras of periodic weighted surface algebras, investigated in [17] and [19].

17 citations

01 Jan 2006
Abstract: First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating congruences on a regular semigroup forms a modular lattice[Theorem 3.6]. Moreover, we prove that the lattice of intuitionistic fuzzy congruences on a regular semigroup is a disjoint union of some modular sublattices of the lattice[Corollary 3.15]. Finally, we show that the lattice of intuitionistic fuzzy congruences on a group and the lattice of intuitionistic fuzzy normal subgroups satisfying the particular condition are lattice isomorphic[Theorem 4.6]. Corresponding author 212 Kul Hur, Su Youn Jang and Hee Won Kang Mathematics Subject Classification: 03F55, 06B10, 06C05

17 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that Brauer graph algebras coincide with the class of indecomposable idempotent biserial weighted surface algesbras, which are associated with triangulated surfaces with arbitrarily oriented triangles.
Abstract: We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated with triangulated surfaces with arbitrarily oriented triangles, investigated recently in Erdmann and Skowronski (J Algebra 505:490–558, 2018, Algebras of generalized dihedral type, Preprint. arXiv:1706.00688, 2017). Moreover, we prove that Brauer graph algebras are idempotent algebras of periodic weighted surface algebras, investigated in Erdmann and Skowronski (Algebras of generalized quaternion type, Preprint. arXiv:1710.09640, 2017).

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023106
2022263
202184
2020100
201991
201892