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Semi-implication algebra. (English) Zbl 0856.08004
The author generalizes the concept of an implication algebra to that of a semi-implication algebra \((A,\cdot)\). \(A\) induces naturally a \(q\)-semilattice. Let \((a, b)\in R\) for \(a, b\in A\) iff \((ab)b= 1b\) and \(B_p= \{a\in A\mid (p, a)\in R\}\) for \(p\in A\). Then every \(B_p\) is a \(q\)-algebra. Further results are on the nilpotent shift of the variety of semilattices and implication algebras.
Reviewer: G.Kalmbach (Ulm)

MSC:
08A62 Finitary algebras
06A12 Semilattices
08B99 Varieties
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