Results 61 to 70 of about 119 (83)

On groups of hypersubstitutions

Algebra universalis, 2010
Let \(\tau : \Omega \to \mathbb{N}\) be a finitary type, where \(\Omega\) is a set of symbols of algebraic operations and \(\tau (\omega )\) is the arity of the \(\omega\). Let \(P\) denote the ordered set of positive integers and \(P\Omega \) denote the set of \(\Omega\)-words over \(P\).
openaire   +1 more source

POWER CLONES AND NON-DETERMINISTIC HYPERSUBSTITUTIONS

Asian-European Journal of Mathematics, 2008
Hypersubstitutions map operation symbols to terms of the corresponding arity. Any hypersubstitution can be extended to a mapping defined on the set Wτ(X) of all terms of type τ. If σ : {fi | i ∈ I} → Wτ(X) is a hypersubstitution and [Formula: see text] its canonical extension, then the set [Formula: see text] is a tree transformation where the ...
Denecke, K., Glubudom, P., Koppitz, J.
openaire   +2 more sources

PROPERTIES OF VARIETIES DETERMINED BY THE DEGREES OF PROPER HYPERSUBSTITUTIONS

Asian-European Journal of Mathematics, 2008
The degree of proper hypersubstitutions is a numerical invariant of a variety. The main problem related to the degree of proper hypersubstitutions is to characterize all varieties of a given type τ which have, for a given positive integer n, this n as degree of proper hypersubstitutions.
Denecke, Klaus, Srithus, Rattana
openaire   +1 more source

The Monoid of Hypersubstitutions of Type (n)

Southeast Asian Bulletin of Mathematics, 2000
A hypersubstitution of type \((n)\) is a map which takes the \(n\)-ary operation symbol to an \(n\)-ary term. It can be inductively extended to a map on the set of all terms of type \((n)\) and two such extensions can be composed in a natural way. Thus the set \(\text{Hyp}(n)\) of all hypersubstitutions of type \((n)\) forms a monoid.
openaire   +2 more sources

Green's Relations on the Monoid of Regular Hypersubstitutions

Algebra Colloquium, 2006
The theory of hyperidentities and hypervarieties is based on the fact that the set Hyp (τ) of all hypersubstitutions of a fixed type τ forms a monoid, with a Galois connection between submonoids of this monoid and complete sublattices of the lattice of all varieties of type τ.
Changphas, Th., Wismath, S. L.
openaire   +1 more source

Valuations and hypersubstitutions

2003
A valuation of a term \(t\) is a non-negative integer which expresses in a certain sense the complexity of \(t\) (it can be the number of operations occurring in \(t\), the number of variables, etc). A hypersubstitution \(\sigma\) is called increasing with respect to a valuation \(v\) if \(v(t)\leq v(\overline\sigma(t))\).
Denecke, Klaus-Dieter, Wismath, Shelly
openaire   +2 more sources

The Order of Hypersubstitutions of Type τ = (3)

Algebra Colloquium, 2006
Hypersubstitutions were introduced in [3] as a way of making precise the concepts of hyperidentity and M-hyperidentity. The monoid of hypersubstitutions has been widely studied by many authors. Knowledge of the monoid of hypersubstitutions can be applied to the concept of M-hyperidentities. In this paper, we show that the order of hypersubstitutions of
openaire   +3 more sources

Deterministic and non-deterministic hypersubstitutions for algebraic systems

Asian-European Journal of Mathematics, 2016
Hypersubstitutions for algebraic systems are mappings which send operation symbols to terms and relational symbols to formulas preserving arities (see [D. Phusanga, Derived Algebraic Systems, Ph.D. thesis, Potsdam (2013)]). In the non-deterministic case, i.e.
Joomwong, Jintana, Phusanga, Dara
openaire   +1 more source

EQUATIONAL THEORIES GENERATED BY HYPERSUBSTITUTIONS OF TYPE (n)

International Journal of Algebra and Computation, 2002
Hypersubstitutions map n-ary operation symbols to n-ary terms. Such mappings can be uniquely extended to mappings defined on the set of all terms. It turns out that the kernels of hypersubstitutions are fully invariant congruence relations on the (absolutely free) term algebra of the considered type. For an arbitrary type τ = (n), n ≥ 1, i.e.
Klaus Denecke, Jörg Koppitz, Staszek Niwczyk   +2 more
openaire   +1 more source

Binary relations on monoids of hypersubstitutions

1997
An equation \(s\approx t\) of terms of type \(\tau\) is a hyperidentity in a variety \(V\) of type \(\tau\) if, whenever the operation symbols occurring in \(s\) and \(t\) are replaced by any terms of the appropriate arity, the resulting equation is an identity in \(V\).
Denecke, Klaus-Dieter, Marszalek, R.
openaire   +2 more sources