A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green’s relations, have been studied for type (n) by S.L. Wismath. A generalized hypersubstitution of type τ=(n) is a mapping σ which takes the n-ary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ=(n), and any two such extensions can be composed in a natural way. Thus, the set of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of . In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green’s relations of this monoid.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1168,
author = {Wattapong Puninagool and Sorasak Leeratanavalee},
title = {The monoid of generalized hypersubstitutions of type $\tau$ = (n)},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {30},
year = {2010},
pages = {173-191},
zbl = {1245.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1168}
}
Wattapong Puninagool; Sorasak Leeratanavalee. The monoid of generalized hypersubstitutions of type τ = (n). Discussiones Mathematicae - General Algebra and Applications, Tome 30 (2010) pp. 173-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1168/
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