In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class of non-trivial subvarieties of the variety of all semilattice ordered modes (modals).
@article{bwmeta1.element.doi-10_2478_s11533-012-0018-6,
author = {Agata Pilitowska and Anna Zamojska-Dzienio},
title = {On some congruences of power algebras},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {987-1003},
zbl = {1258.08002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0018-6}
}
Agata Pilitowska; Anna Zamojska-Dzienio. On some congruences of power algebras. Open Mathematics, Tome 10 (2012) pp. 987-1003. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0018-6/
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