Subdirectly irreducible sectionally pseudocomplemented semilattices

Author: Halaš R.  

Publisher: Springer Publishing Company

ISSN: 0011-4642

Source: Czechoslovak Mathematical Journal, Vol.57, Iss.2, 2007-06, pp. : 725-735

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Abstract

Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.