Premium
Idempotent n ‐permutable varieties
Author(s) -
Valeriote M.,
Willard R.
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu044
Subject(s) - permutable prime , mathematics , idempotence , variety (cybernetics) , distributive property , class (philosophy) , congruence (geometry) , combinatorics , pure mathematics , discrete mathematics , algebra over a field , computer science , artificial intelligence , statistics , geometry
One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n ‐permutable for some n . In 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 n ‐permutable for some n if and only if it interprets an idempotent variety that is not interpretable in the variety of distributive lattices.