The monoid of generalized hypersubstitutions of type τ = (n)

Wattapong Puninagool, and Sorasak Leeratanavalee. "The monoid of generalized hypersubstitutions of type τ = (n)." Discussiones Mathematicae - General Algebra and Applications 30.2 (2010): 173-191. <http://eudml.org/doc/276468>.

@article{WattapongPuninagool2010,
abstract = {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 $Hyp_\{G\}(n)$ of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of $Hyp_\{G\}(n)$. In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green’s relations of this monoid.},
author = {Wattapong Puninagool, Sorasak Leeratanavalee},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {monoid; regular elements; idempotent elements; Green's relations; generalized hypersubstitution},
language = {eng},
number = {2},
pages = {173-191},
title = {The monoid of generalized hypersubstitutions of type τ = (n)},
url = {http://eudml.org/doc/276468},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Wattapong Puninagool
AU - Sorasak Leeratanavalee
TI - The monoid of generalized hypersubstitutions of type τ = (n)
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 2
SP - 173
EP - 191
AB - 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 $Hyp_{G}(n)$ of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of $Hyp_{G}(n)$. In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green’s relations of this monoid.
LA - eng
KW - monoid; regular elements; idempotent elements; Green's relations; generalized hypersubstitution
UR - http://eudml.org/doc/276468
ER -