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Subdirect decompositions of algebras from 2-clone extensions of varieties

J. Płonka (1998)

Colloquium Mathematicae

Let τ:F → ℕ be a type of algebras, where F is a set of fundamental operation symbols and ℕ is the set of nonnegative integers. We assume that |F|≥2 and 0 ∉ (F). For a term φ of type τ we denote by F(φ) the set of fundamental operation symbols from F occurring in φ. An identity φ ≉ ψ of type τ is called clone compatible if φ and ψ are the same variable or F(φ)=F(ψ)≠ . For a variety V of type τ we denote by V c , 2 the variety of type τ defined by all identities φ ≉ ψ from Id(V) which are either clone compatible...

Super-De Morgan functions and free De Morgan quasilattices

Yuri Movsisyan, Vahagn Aslanyan (2014)

Open Mathematics

A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....

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