Distinguishing subsets in semilattices
Josef Zapletal (1973)
Archivum Mathematicum
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Josef Zapletal (1973)
Archivum Mathematicum
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Jaroslav Ježek, Tomáš Kepka (2009)
Czechoslovak Mathematical Journal
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We prove that the semirings of 1-preserving and of 0,1-preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.
Ivan Chajda (2002)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Radomír Halaš, Jan Kühr (2007)
Czechoslovak Mathematical Journal
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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...
S. N. Begum, Abu Saleh Abdun Noor (2011)
Mathematica Bohemica
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A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.