@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}
}