# On some congruences of power algebras

Agata Pilitowska; Anna Zamojska-Dzienio

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 987-1003
- ISSN: 2391-5455

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topAgata Pilitowska, and Anna Zamojska-Dzienio. "On some congruences of power algebras." Open Mathematics 10.3 (2012): 987-1003. <http://eudml.org/doc/269105>.

@article{AgataPilitowska2012,

abstract = {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).},

author = {Agata Pilitowska, Anna Zamojska-Dzienio},

journal = {Open Mathematics},

keywords = {Idempotent; Entropic; Modes; Power algebras; Congruence relations; Identities; Finitary algebras; idempotent algebra; entropic algebra; mode; modal; power algebra; congruence relation; identity; finitary algebra; idempotent quotient},

language = {eng},

number = {3},

pages = {987-1003},

title = {On some congruences of power algebras},

url = {http://eudml.org/doc/269105},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Agata Pilitowska

AU - Anna Zamojska-Dzienio

TI - On some congruences of power algebras

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 987

EP - 1003

AB - 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).

LA - eng

KW - Idempotent; Entropic; Modes; Power algebras; Congruence relations; Identities; Finitary algebras; idempotent algebra; entropic algebra; mode; modal; power algebra; congruence relation; identity; finitary algebra; idempotent quotient

UR - http://eudml.org/doc/269105

ER -

## References

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