R. Halas, J. Kuhr, Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: email@example.com, firstname.lastname@example.org
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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