@article{WismathKoppitzDenecke1997,
  author    = {Wismath, Shelly and Koppitz, J{\"o}rg and Denecke, Klaus-Dieter},
  title     = {Maps between M-solid varieties of emigroups},
  year      = {1997},
  language  = {en}
}
@article{DeneckeWismath1997,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {The monoid of hypersubstitutions of type (2)},
  year      = {1997},
  language  = {en}
}
@article{DeneckeWismath2009,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {The dimension of a variety and the kernel of a hypersubstitution},
  issn      = {0218-1967},
  doi       = {10.1142/S0218196709005342},
  year      = {2009},
  abstract  = {The dimension of a variety V of algebras of a given type was introduced by E. Graczynska and D. Schweigert in [7] as the cardinality of the set of all derived varieties of V which are properly contained in V. In this paper, we characterize all solid varieties of dimensions 0, 1, and 2; prove that the dimension of a variety of finite type is at most N-0; give an example of a variety which has infinite dimension; and show that for every n is an element of N there is a variety with dimension n. Finally, we show that the dimension of a variety is related to the concept of the semantical kernel of a hypersubstitution and apply this connection to calculate the dimension of the class of all algebras of type tau = (n).},
  language  = {en}
}
@article{DeneckeWismath1994,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Solid varieties of semigroups},
  year      = {1994},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Complexity of Terms, Composition and Hypersubstitution},
  year      = {2003},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Valuations and Hypersubstitutions},
  year      = {2003},
  language  = {en}
}
@book{DeneckeWismath2000,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Hyperidentities and clones},
  series = {Algebra, logic and aplications},
  volume    = {14},
  journal   = {Algebra, logic and aplications},
  publisher = {Gordon \& Breach},
  address   = {Amsterdam},
  isbn      = {90-5699-235-X},
  pages     = {XI, 314 S. : graph. Darst.},
  year      = {2000},
  abstract  = {The theory of hyperidentities generalises the equational theory of universal algebras and is applicable in several fields of science, especially in computer sciences. This book presents the theory of hyperidentities and its relation to clone identities. The basic concept of hypersubstitution is used to introduce the monoid of hypersubstitutions, hyperidentities, M-hyperidentities, solid and M-solid varieties. This work integrates into a coherent framework many results scattered throughout the literature over the last eighteen years. In addition, the book contains some applications of hyperidentities to the functional completenes problem in multiple-valued logic. The general theory is also extended to partial algberas. The last chapter contains a list of exercises and open problems with suggestions of future work in this area of research.},
  language  = {en}
}
@article{DeneckeWismath2003,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Valuations of Terms},
  year      = {2003},
  abstract  = {Let tau be a type of algebras. There are several commonly used measurements of the complexity of terms of type tau, including the depth or height of a term and the number of variable symbols appearing in a term. In this paper we formalize these various measurements, by defining a complexity or valuation mapping on terms. A valuation of terms is thus a mapping from the absolutely free term algebra of type tau into another algebra of the same type on which an order relation is defined. We develop the interconnections between such term valuations and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; valuations of terms offer a new method to study complete sublattices of this lattice},
  language  = {en}
}
@book{DeneckeWismath2002,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {Universal algebra and applications in theoretical computer science},
  publisher = {Chapman \& Hall/CRC},
  address   = {Boca Raton},
  isbn      = {1-584-88254-9},
  pages     = {383 S.},
  year      = {2002},
  language  = {en}
}
@article{DeneckeWismath2002,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {M-solidity testing systems},
  year      = {2002},
  language  = {en}
}
@article{DeneckeWismath2004,
  author    = {Denecke, Klaus-Dieter and Wismath, Shelly},
  title     = {A characterization of k-normal varieties},
  issn      = {0002-5240},
  year      = {2004},
  abstract  = {Let v be a valuation of terms of type tau, assigning to each term t of type tau a value v(t) greater than or equal to 0. Let k greater than or equal to 1 be a natural number. An identity s approximate to t of type tau is called k- normal if either s = t or both s and t have value greater than or equal to k, and otherwise is called non-k-normal. A variety V of type tau is said to be k-normal if all its identities are k-normal, and non-k-normal otherwise. In the latter case, there is a unique smallest k-normal variety N-k(A) (V) to contain V , called the k-normalization of V. Inthe case k = 1, for the usual depth valuation of terms, these notions coincide with the well-known concepts of normal identity, normal variety, and normalization of a variety. I. Chajda has characterized the normalization of a variety by means of choice algebras. In this paper we generalize his results to a characterization of the k-normalization of a variety, using k-choice algebras. We also introduce the concept of a k-inflation algebra, and for the case that v is the usual depth valuation of terms, we prove that a variety V is k-normal iff it is closed under the formation of k- inflations, and that the k-normalization of V consists precisely of all homomorphic images of k-inflations of algebras in V},
  language  = {en}
}
@article{DeneckeKoppitzWismath2001,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Wismath, Shelly},
  title     = {The semantical hyperunification problem},
  year      = {2001},
  language  = {en}
}
@article{DeneckeKoppitzWismath2002,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg and Wismath, Shelly},
  title     = {Solid Varietie of Arbitrary Type},
  year      = {2002},
  language  = {en}
}
@article{DeneckeJampachonWismath2003,
  author    = {Denecke, Klaus-Dieter and Jampachon, Prakit and Wismath, Shelly},
  title     = {Clones of n-ary algebras},
  year      = {2003},
  language  = {en}
}