@phdthesis{ArwornDenecke1999,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Sets of hypersubstitutions and set-solid varieties},
  year      = {1999},
  language  = {en}
}
@article{ArwornDenecke1999,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Left-edges solid varieties of differential groupoids},
  year      = {1999},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Groupoids of hypersubstitutions and G-solid varieties},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {A new methods to study subvariety lattices of semigroup varieties},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke2001,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Tree Transformations defined by Hypersubstitutions},
  issn      = {1509 - 9415},
  year      = {2001},
  language  = {en}
}
@article{ArwornDenecke2002,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {Intervals and complete congruences defined by M-solid varieties},
  year      = {2002},
  language  = {en}
}
@article{ArwornDeneckeKoppitz2001,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Strongly luid and weakly unsolid varieties},
  issn      = {1346-0862},
  year      = {2001},
  language  = {en}
}
@book{ArwornDeneckePoeschel1998,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter and P{\"o}schel, Reinhard},
  title     = {Closure operators on complete lattices},
  series = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden},
  volume    = {1998, 05},
  journal   = {Preprint MATH-ALG / Technische Universit{\"a}t Dresden},
  publisher = {Techn. Univ.},
  address   = {Dresden},
  year      = {1998},
  language  = {en}
}
@article{ChajadaDeneckeHalas1999,
  author    = {Chajada, I. and Denecke, Klaus-Dieter and Halas, R.},
  title     = {Algebras induced by hypersubstitutions},
  year      = {1999},
  language  = {en}
}
@article{ChangphasDenecke2005,
  author    = {Changphas, Thawhat and Denecke, Klaus-Dieter},
  title     = {Green's relation R on the monoid of clone endomorphisms},
  issn      = {1005-3867},
  year      = {2005},
  abstract  = {A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set W-tau(X) of all terms of type tau, and any two such extensions can be composed in a natural way. Thus, the set Hyp(tau) of all hypersubstitutions of type tau forms a monoid. In this paper, we characterize Green's relation R on the monoid Hyp(tau) for the type tau = (n, n). In this case, the monoid of all hypersubstitutions is isomorphic with the monoid of all Clone endomorphisms. The results can be applied to mutually derived varieties},
  language  = {en}
}
@article{ChangphasDenecke2003,
  author    = {Changphas, Thawhat and Denecke, Klaus-Dieter},
  title     = {Green's Relations on the Seminearring of Full Hypersubstitutions of Type (n)},
  year      = {2003},
  language  = {en}
}
@article{ChangphasDenecke2003,
  author    = {Changphas, Thawhat and Denecke, Klaus-Dieter},
  title     = {Complexity of Hypersubstitutions and Lattices of Varieties},
  year      = {2003},
  language  = {en}
}
@article{Denecke1999,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones closed with respect to closed operators},
  year      = {1999},
  language  = {en}
}
@article{Denecke1995,
  author    = {Denecke, Klaus-Dieter},
  title     = {Hybrid identities and hybrid equational logic},
  year      = {1995},
  language  = {en}
}
@article{Denecke1995,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and hyperidentities},
  year      = {1995},
  language  = {en}
}
@article{Denecke2019,
  author    = {Denecke, Klaus-Dieter},
  title     = {The partial clone of linear formulas},
  series = {Siberian mathematical journal},
  volume    = {60},
  journal   = {Siberian mathematical journal},
  number    = {4},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446619040037},
  pages     = {572 -- 584},
  year      = {2019},
  abstract  = {A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).},
  language  = {en}
}
@article{Denecke1996,
  author    = {Denecke, Klaus-Dieter},
  title     = {The entropy sequence of unary logical functions},
  year      = {1996},
  language  = {en}
}
@article{Denecke1997,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and Hyperidentities},
  year      = {1997},
  language  = {en}
}
@book{Denecke1996,
  author    = {Denecke, Klaus-Dieter},
  title     = {Clones and hyperidentities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1996, 14},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {33 Bl.},
  year      = {1996},
  language  = {en}
}
@article{Denecke2016,
  author    = {Denecke, Klaus-Dieter},
  title     = {The partial clone of linear terms},
  series = {Siberian Mathematical Journal},
  volume    = {57},
  journal   = {Siberian Mathematical Journal},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446616040030},
  pages     = {589 -- 598},
  year      = {2016},
  abstract  = {Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type tau, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Congruences on maximal partial clones and strong regular varieties generated by preprimal partial algebras II},
  year      = {1991},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Strong regular varieties of partial algebras I},
  year      = {1991},
  language  = {en}
}
@article{Denecke1991,
  author    = {Denecke, Klaus-Dieter},
  title     = {Minimal algebras and category equivalences},
  year      = {1991},
  language  = {en}
}
@article{Denecke1998,
  author    = {Denecke, Klaus-Dieter},
  title     = {Tame congruence theory},
  year      = {1998},
  language  = {en}
}
@book{Denecke1997,
  author    = {Denecke, Klaus-Dieter},
  title     = {Hyperequational theory},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 29},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {33 Bl.},
  year      = {1997},
  language  = {en}
}
@article{Denecke1994,
  author    = {Denecke, Klaus-Dieter},
  title     = {On the characterization of primal partial algebras by strong regular hyperidentities},
  year      = {1994},
  language  = {en}
}
@article{Denecke1994,
  author    = {Denecke, Klaus-Dieter},
  title     = {Pre-solid varieties},
  year      = {1994},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {Solid polynomial varieties of semigroups which are definable by identities},
  isbn      = {3-85366-951-4},
  year      = {2000},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {Generalized hypersubstitutions and strongly solid varieties},
  isbn      = {3-8265- 7983-6},
  year      = {2000},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {P-compatible hypersubstitutions and M_P -solid varieties},
  year      = {2000},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {Fluid, unsolid, and completely unsolid varieties},
  year      = {2000},
  language  = {en}
}
@article{Denecke2001,
  author    = {Denecke, Klaus-Dieter},
  title     = {Hyperidentities in semigroups},
  isbn      = {90-5199-490-7},
  year      = {2001},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {The galois correspondence between subvariety lattices and monoids of hypersubstitutions},
  year      = {2000},
  language  = {en}
}
@article{Denecke2020,
  author    = {Denecke, Klaus-Dieter},
  title     = {Partial clones},
  series = {Asian-European journal of mathematics : AEJM},
  volume    = {13},
  journal   = {Asian-European journal of mathematics : AEJM},
  number    = {8},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557120501612},
  pages     = {19},
  year      = {2020},
  abstract  = {A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.},
  language  = {en}
}
@article{Denecke2000,
  author    = {Denecke, Klaus-Dieter},
  title     = {Solid varieties of normal ID-semirings},
  isbn      = {3-8265- 7983-6},
  year      = {2000},
  language  = {en}
}
@article{DeneckeArworn2000,
  author    = {Denecke, Klaus-Dieter and Arworn, Srichan},
  title     = {Intervals defined by M-solid varieties},
  isbn      = {3-8265- 7983-6},
  year      = {2000},
  language  = {en}
}
@article{DeneckeChangphas2003,
  author    = {Denecke, Klaus-Dieter and Changphas, Thawhat},
  title     = {Full hypersubstitutions and fully solid varieties of semigroups},
  year      = {2003},
  language  = {en}
}
@article{DeneckeFreiberg1998,
  author    = {Denecke, Klaus-Dieter and Freiberg, L.},
  title     = {The word problem for M-solid varieties of semigroups},
  isbn      = {981-3083-86-7},
  year      = {1998},
  language  = {en}
}
@article{DeneckeHalkowska1994,
  author    = {Denecke, Klaus-Dieter and Halkowska, Katarzcyna},
  title     = {P-compatible hybrid-identities and hyperidentities},
  year      = {1994},
  language  = {en}
}
@article{DeneckeHounnon2021,
  author    = {Denecke, Klaus-Dieter and Hounnon, Hippolyte},
  title     = {Partial Menger algebras of terms},
  series = {Asian-European journal of mathematics},
  volume    = {14},
  journal   = {Asian-European journal of mathematics},
  number    = {06},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557121500923},
  pages     = {14},
  year      = {2021},
  abstract  = {The superposition operation S-n,S-A, n >= 1, n is an element of N, maps to each (n + 1)-tuple of n-ary operations on a set A an n-ary operation on A and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank n. A partial algebra of type (n + 1) which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank n. As a generalization of linear terms we define r-terms as terms where each variable occurs at most r-times. It will be proved that n-ary r-terms form partial Menger algebras of rank n. In this paper, some algebraic properties of partial Menger algebras such as generating systems, homomorphic images and freeness are investigated. As generalization of hypersubstitutions and linear hypersubstitutions we consider r-hypersubstitutions.U},
  language  = {en}
}
@article{DeneckeHounnon2003,
  author    = {Denecke, Klaus-Dieter and Hounnon, Hippolyte},
  title     = {All solid varieties of semirings},
  year      = {2003},
  language  = {en}
}
@article{DeneckeHounnon2000,
  author    = {Denecke, Klaus-Dieter and Hounnon, Hippolyte},
  title     = {Solid varieties of normal ID-semirings},
  isbn      = {3-8265- 7983-6},
  year      = {2000},
  language  = {en}
}
@article{DeneckeHounnon2000,
  author    = {Denecke, Klaus-Dieter and Hounnon, Hippolyte},
  title     = {Solid varieties of semirings},
  isbn      = {981-02-4392-8},
  year      = {2000},
  language  = {en}
}
@article{DeneckeJampachon1999,
  author    = {Denecke, Klaus-Dieter and Jampachon, Prakit},
  title     = {Regular-solid varieties of commutative and idempotent groupoids},
  year      = {1999},
  language  = {en}
}
@article{DeneckeJampachon2003,
  author    = {Denecke, Klaus-Dieter and Jampachon, Prakit},
  title     = {N-solid Varieties and free Menger Algebras of rRnk n},
  year      = {2003},
  language  = {en}
}
@article{DeneckeJampachonWismath2003,
  author    = {Denecke, Klaus-Dieter and Jampachon, Prakit and Wismath, Shelly},
  title     = {Clones of n-ary algebras},
  year      = {2003},
  language  = {en}
}
@article{DeneckeKoppitz1999,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Normal forms of hypersubstitutions},
  year      = {1999},
  language  = {en}
}
@article{DeneckeKoppitz1998,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Finite monoids of hypersubstitutions of type € = (2)},
  year      = {1998},
  language  = {en}
}
@article{DeneckeKoppitz1995,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {Pre-solid varieties of commutative semigroups},
  year      = {1995},
  language  = {en}
}
@article{DeneckeKoppitz1995,
  author    = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg},
  title     = {M-solid varieties of semigroups},
  year      = {1995},
  language  = {en}
}