Order in Implication Zroupoids
Juan M. Cornejo, Hanamantagouda P. Sankappanavar

TL;DR
This paper investigates the structure of implication zroupoids, identifying a maximal subvariety where a certain order relation is a partial order, and counts the number of non-isomorphic chains within this subvariety.
Contribution
It establishes that the subvariety ,0,0, is maximal for the partial order property and determines the exact number of non-isomorphic ,0,0-chains of size n for each natural number n.
Findings
,0,0 is a maximal subvariety with the partial order property.
Number of non-isomorphic ,0,0-chains of size n is exactly n.
Provides a classification of chains in the subvariety ,0,0.
Abstract
The variety of implication zroupoids was defined and investigated by Sankappanavar ([7]) as a generalization of De Morgan algebras. Also, in [7], several new subvarieties of were introduced, including the subvariety , defined by the identity: , which plays a crucial role in this paper. Several more new subvarieties of , including the subvariety of semilattices with a least element , are studied in [3], and an explicit description of semisimple subvarieties of is given in [5]. It is well known that the operation induces a partial order () in the variety and also in the variety of De Morgan algebras. As both and are subvarieties of and the definition of partial order can be expressed in terms of the…
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · Rough Sets and Fuzzy Logic
