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періодичних видань НАН України
Algebra in superextensions of semilattices
Репозиторій DSpace/Manakin
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Algebra in superextensions of semilattices
Інший ID:
2010 Mathematics Subject Classification: 06A12, 20M10.
Посилання:
Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ.
Підтримка:
The first author has been partially financed by NCN means granted by decision DEC-2011/01/B/ST1/01439.
Дата:
2012
Переглядів:
517
Завантажень:
156
Анотація:
Given a semilattice X we study the algebraic properties of the semigroup υ(X) of upfamilies on X. The semigroup υ(X) contains the Stone-ˇCech extension β(X), the superextension λ(X), and the space of filters φ(X) on X as closed subsemigroups. We prove that υ(X) is a semilattice iff λ(X) is a semilattice iff φ(X) is a semilattice iff the semilattice X is finite and linearly ordered. We prove that the semigroup β(X) is a band if and only if X has no infinite antichains, and the semigroup λ(X) is commutative if and only if X is a bush with finite branches.
