Mathematicae General Algebra and Applications 20(1) (2000) 87-95
RING-LIKE OPERATIONS IN PSEUDOCOMPLEMENTED SEMILATTICES
Department of Algebra and Geometry, Palacký
Technische Universität Wien, Institut für Algebra
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Keywords: pseudocomplemented semilattice, Boolean algebra, Boolean ring, distributivity, linear equation, ideal, congruence kernel.
1991 Mathematics Subject Classification: 06A12, 08C10, 06E20, 16Y99.
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Received 21 September 1998
Revised 7 June 1999