Geodesic
M-solid generalized non-deterministic varieties
Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 25-43

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A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.
Keywords: generalized non-deterministic hypersubstitution, conjugate pair of additive closure operators, M-solid generalized non-deterministic variety 
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Lekkoksung, Somsak. M-solid generalized non-deterministic varieties. Discussiones Mathematicae. General Algebra and Applications, Tome 36 (2016) no. 1, pp. 25-43. http://geodesic.mathdoc.fr/item/DMGAA_2016_36_1_a2/