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 given a finite idempotent algebra A in a finite language, there is a polynomial-time algorithm that determines whether the variety generated by A is n-permutable.
Abstract: One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n-permutable for some n .I n this paper, we prove two results: (1) for every n> 1, there is a polynomial-time algorithm that, given a finite idempotent algebra A in a finite language, determines whether the variety generated by A is n-permutable and (2) a variety is npermutable for some n if and only if it interprets an idempotent variety that is not interpretable in the variety of distributive lattices.
20 citations
TL;DR: A primitive symmetric association scheme of class 2 is naturally embedded as a two-distance set in the unit sphere of Euclidean space, with respect to the primitive idempotent E1 of the Bose-Mesner algebra of the association scheme.
Abstract: A primitive symmetric association scheme of class 2 is naturally embedded as a two-distance set in the unit sphere of Euclidean space, with respect to the primitive idempotent E1 of the Bose-Mesner algebra of the association scheme. Then it is shown that the ratio of the two distances of the two-distance set is instantly read from the character table (i.e., the first eigen matrix P) of the association scheme.
20 citations
TL;DR: It is shown that the free model of the new set of axioms is a class of trees labelled over A, and the three proposed interpretations of regular expressions (algebraic, denotational, and behavioural) are proven to coincide.
19 citations
TL;DR: It is shown that idempotent uninorms are in one-to-one correspondence with special linear orders on 0 , 1 and the characterizing multi-function of the uninorm is investigated.
19 citations
19 citations