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Ring-like operations in pseudocomplemented semilattices. (English) Zbl 0968.06004
The authors introduce ring-like operations in pseudocomplemented semilattices. In case of Boolean pseudocomplemented semilattices we can obtain 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 are given. Finally they define ideals in the ring-like structures.

MSC:
06A12 Semilattices
08C10 Axiomatic model classes
06E20 Ring-theoretic properties of Boolean algebras
16Y99 Generalizations
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