Idempotent  n ‐permutable varieties | Zendy

Valeriote M. | Zendy; Willard R. | Zendy

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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.

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