Document Zbl 0968.06004

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Ring-like operations in pseudocomplemented semilattices. (English) Zbl 0968.06004

Discuss. Math., Gen. Algebra Appl. 20, No. 1, 87-95 (2000).

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.

Reviewer: Renata Majovská (Horní Suchá)

Cited in 2 Documents

MSC:

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

Keywords:

pseudocomplemented semilattices; Boolean algebra; Boolean ring; distributivity; linear equation; ideal; congruence kernel

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