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- W3085802105 abstract "Abstract In 2012, the second author introduced, and initiated the investigations into, the variety ๐ of implication zroupoids that generalize De Morgan algebras and โจ-semilattices with 0. An algebra A = ใ A , โ, 0 ใ, where โ is binary and 0 is a constant, is called an implication zroupoid (๐-zroupoid, for short) if A satisfies: ( x โ y ) โ z โ [( z โฒ โ x ) โ ( y โ z )โฒ]โฒ, where x โฒ := x โ 0, and 0โณ โ 0. Let ๐ denote the variety of implication zroupoids and A โ ๐. For x , y โ A , let x โง y := ( x โ y โฒ)โฒ and x โจ y := ( x โฒ โง y โฒ)โฒ. In an earlier paper, we had proved that if A โ ๐, then the algebra A mj = ใ A , โจ, โงใ is a bisemigroup. The purpose of this paper is two-fold: First, we generalize the notion of semidistributivity from lattices to bisemigroups and prove that, for every A โ ๐, the bisemigroup A mj is semidistributive. Secondly, we generalize the Whitman Property from lattices to bisemigroups and prove that the subvariety ๐๐๐ of ๐, defined by the identity: x โง y โ x โจ y , satisfies the Whitman Property. We conclude the paper with two open problems." @default.
- W3085802105 created "2020-09-21" @default.
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- W3085802105 date "2021-12-01" @default.
- W3085802105 modified "2023-10-18" @default.
- W3085802105 title "Semidistributivity and Whitman Property in implication zroupoids" @default.
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- W3085802105 doi "https://doi.org/10.1515/ms-2021-0056" @default.
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