Subdirectly irreducible sectionally pseudocomplemented semilattices
نویسندگان
چکیده
منابع مشابه
Subdirectly irreducible semilattices with an automorphism
In other words, SA is the variety of semilattices with one automorphism (which is, as well as its inverse, considered as an additional fundamental operation). The aim of this paper is to find all subdirectly irreducible algebras in SA . A universal algebra A is said to be subdirectly irreducible (shortly, an SI algebra) if it contains more than one element and among all the nontrivial congruenc...
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At first, we recall the basic concept, By a residual lattice is meant an algebra ) 1 , 0 , , , , , ( o ∗ ∧ ∨ = L L such that (i) ) 1 , 0 , , , ( ∧ ∨ = L L is a bounded lattice, (ii) ) 1 , , ( ∗ = L L is a commutative monoid, (iii) it satisfies the so-called adjoin ness property: y z y x = ∗ ∨ ) ( if and only if y x z y o ≤ ≤ Let us note [7] that y x ∨ is the greatest element of the set y z y x ...
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A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...
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A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...
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We study ∨-semilattices with the greatest element 1 where on each interval [a,1] an antitone bijection is defined. We characterize these semilattices by means of two induced binary operations proving that the resulting algebras form a variety. The congruence properties of this variety and the properties of the underlying semilattices are investigated. We show that this variety contains a single...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2007
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-007-0109-x