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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
EN
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].
2
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Hyperidentities in associative graph algebras

100%
Poomsa-ard T.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 2
169-182
EN
Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A. In this paper we characterize associative graph algebras, identities in associative graph algebras and hyperidentities in associative graph algebras.
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The greatest regular-solid variety of semigroups % Dedicated to R. McKenzie's 60$^th$ birthday %

88%
Denecke K., Koppitz J., Pabhapote N.
Discussiones Mathematicae - General Algebra and Applications
|
2008
|
tom 28
|
nr 1
91-119
EN
A regular hypersubstitution is a mapping which takes every $n_i$-ary operation symbol to an $n_i$-ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities.
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