Results 211 to 220 of about 597,740 (256)

All Solid Varieties of Semirings

Journal of Algebra, 2002
A hypersubstitution results from a substitution of each operation symbol by a term of the same arity. A variety \(V\) is called solid if for every identity \(s\approx t\) which holds in \(V\) and every hypersubstitution, the identity which is obtained from \(s\approx t\) by applying the hypersubstitution is again satisfied in \(V\). A semiring \(S\) is
K Denecke
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Solid varieties of arbitrary type

Algebra Universalis, 2002
A variety is solid if each of its identities holds as a hyperidentity, i.e., if it is satisfied also whenever the fundamental operations are replaced by terms of the same arity. Although an infinite number of solid varieties of semigroups is known, only very few examples of solid varieties are known for other similarity types.
Jörg Koppitz
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All Solid Varieties of Semigroups

Journal of Algebra, 1999
An identity \(u=v\) is said to be a hyperidentity in a variety \(\mathcal V\) if \(\mathcal V\) hypersatisfies \(u=v\) in the sense that whenever the operation symbols occurring in the terms \(u\) and \(v\) are replaced by any term (of the same type) of the appropriate arity, \(\mathcal V\) satisfies the resulting identity. A variety is called solid if
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Solid varieties of semigroups

Semigroup Forum, 1994
Let \(\tau = (n_ i)_{i \in I}\) be a type and \((f_ i)_{i \in I}\) operation symbols such that the arity of \(f_ i\) is \(n_ i\). Let \(W_ \tau(X)\) be the set of all terms of type \(\tau\) in an alphabet \(X\). A map \(\sigma: (f_ i)_{i \in I} \to W_{\tau}(X)\) is a hypersubstitution.
S L Wismath, K Denecke
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SOLID VARIETIES OF SEMIRINGS

Semigroups, 2000
Klaus Denecke
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M-solid varieties generated by lattices

Algebra Universalis, 2000
An identity \(p=q\) is hypersatisfied by a variety \({\mathcal V}\) whenever \({\mathcal V}\models \tau (p)=\tau (q)\) for every hypersubstitution \(\tau \) (a mapping substituting operation symbols by arbitrary terms of appropriate arity). Whenever \(p=q\) is hypersatisfied in \({\mathcal V}\), it is called a hyperidentity of \({\mathcal V}\).
R Padmanabhan
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On existence varieties of E-solid semigroups

SemiGroup Forum, 1999
This paper contains deep results in the theory of existence varieties of regular semigroups. First of all, a suitable equational logic for e-varieties of \(E\)-solid semigroups is developed which extends the one for orthodox semigroups presented by the same authors [in Semigroup Forum 40, No. 3, 257-296 (1990; Zbl 0705.20052)].
Kaďourek, Jiří, Szendrei, Mária B.
openaire   +4 more sources

All Reg-solid varieties of commutative semigroups

Semigroup Forum, 2008
The author denotes by \(W(X)\) the set of all terms formed from a binary operation symbol \(f\) and the set \(X\) of variables. A hypersubstitution \(\sigma\) of type (2) is defined by specifying a term \(\sigma(f)\in W(\{x_1,x_2\})\); it is called regular if both variables \(x_1\) and \(x_2\) occur in the term \(\sigma(f)\). Every hypersubstitution \(\
Jörg Koppitz
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Hyperidentities and solid varieties

Algebra Universalis, 2006
Let V be a variety of type τ. A type τ hyperidentity of V is an identity of V which also holds in an additional stronger sense: for every substitution of terms of the variety (of appropriate arity) for the operation symbols in the identity, the resulting equation holds as an identity of the variety.
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P-Compatible Hypersubstitution and MP-Solid Varieties

Studia Logica, 2000
The authors consider hypersubstitutions which are compatible with a partition \(P\) of the set of operations, and a corresponding generalized equational theory for \(P\)-compatible hyperidentities is developed.
K. Hlkowska, Klaus Denecke
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