A non-deterministic hypersubstitution maps any operation symbol of a tree language of type τ to a set of trees of the same type, i.e. to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities. We define the application of a non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras. Non-deterministic hypersubstitutions can also be applied to equations of type τ. Formally, we obtain two closure operators which turn out to form a conjugate pair of completely additive closure operators. This allows us to use the theory of conjugate pairs of additive closure operators for a characterization of M-solid non-deterministic varieties of algebras. As an application we consider M-solid non-deterministic varieties of semigroups.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1129,
author = {Klaus Denecke and Prisana Glubudom},
title = {Nd-solid varieties},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {245-262},
zbl = {1147.08002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1129}
}
Klaus Denecke; Prisana Glubudom. Nd-solid varieties. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 245-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1129/
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