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Title: | Finitely Related Clones and Algebras with Cube Terms | Authors: | Marković Petar Maróti Miklós McKenzie Ralph |
Keywords: | Finitely related clonesCube termsAlgebras with few subpowersValeriote’s conjecture | Issue Date: | 2012 | Journal: | Order: A Journal on the Theory of Ordered Sets and its Applications | Abstract: | Aichinger et al. (2011) have proved that every finite algebra with a cube-term (equivalently, with a parallelogram-term; equivalently, having few subpowers) is finitely related. Thus finite algebras with cube terms are inherently finitely related—every expansion of the algebra by adding more operations is finitely related. In this paper, we show that conversely, if A is a finite idempotent algebra and every idempotent expansion of A is finitely related, then A has a cube-term. We present further characterizations of the class of finite idempotent algebras having cube-terms, one of which yields, for idempotent algebras with finitely many basic operations and a fixed finite universe A, a polynomial-time algorithm for determining if the algebra has a cube-term. We also determine the maximal non-finitely related idempotent clones over A. The number of these clones is finite. | URI: | https://open.uns.ac.rs/handle/123456789/28524 | ISSN: | 0167-8094 | DOI: | 10.1007/s11083-011-9232-2 |
Appears in Collections: | PMF Publikacije/Publications |
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