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On Quotient Algebras of Normal Eo-algebras by Congruences
Mayuka F. Kawaguchi and Michiro Kondo
In this paper, we consider properties of quotient algebras of normal eoalgebras. The class of all normal eo-algebras does not form a variety. Normal eo-algebras are weak extended order algebras with two additional normality axioms. We show that (i) there is a one to one correspondence between the set of all closed filters and the set of all closed congruences and (ii) every normal eo-algebra 𝑋 is isomorphic to a subdirect product of subdirectly irreducible normal eo-algebras {𝑋/𝑃𝑎}𝑎 ∈ 𝑋 , where 𝑃𝑎 is a maximal element of closed filters not containing 𝑎 ∈ 𝑋.
Keywords: (closed) congruence, (closed) filter, normal extended-order algebra, BCK-algebra, quotient algebra, subdirect product, subdirectly irreducible