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The order of normalform hypersubstitutions of type (2)

100%

Denecke K., Mahdavi K.

Discussiones Mathematicae - General Algebra and Applications

2000

tom 20

nr 2

183-192

In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].

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

88%

Puninagool W., Leeratanavalee S.

Discussiones Mathematicae - General Algebra and Applications

2010

tom 30

nr 2

173-191

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.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

1 Denecke K.

1 Leeratanavalee S.

1 Mahdavi K.

1 Puninagool W.

1 2010

1 2000

Wyniki wyszukiwania

The order of normalform hypersubstitutions of type (2)

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