Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 725-735, 2007

Subdirectly irreducible sectionally pseudocomplemented semilattices

R. Halas, J. Kuhr

R. Halas, J. Kuhr, Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: halas@inf.upol.cz, kuhr@inf.upol.cz

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.

Keywords: sectionally pseudocomplemented semilattice, weakly standard element

Classification (MSC 2000): 06A12, 06D15


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