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A construction for pseudocomplemented semilattices and two applications. (English) Zbl 0695.06004

A method is given for constructing pseudocomplemented semilattices from graphs. By applying this method, two results are obtained. One is that there exist continuum many quasivarieties of pseudocomplemented semilattices. Another one is that for any non-zero cardinal \(\kappa\), there exists a family of pairwise non-isomorphic pseudocomplemented semilattices with isomorphic endomorphism monoids and that the cardinality of the family is \(2^{\kappa}\) (resp. \(\kappa)\) if \(\kappa\) is infinite (resp. finite).
Reviewer: H.Yutani

MSC:

06A12 Semilattices
08A35 Automorphisms and endomorphisms of algebraic structures
08C15 Quasivarieties
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