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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