TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - The partial clone of linear terms
JF  - Siberian Mathematical Journal
N2  - 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.
KW  - linear term
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
KW  - linear identity
KW  - linear hyperidentity
Y1  - 2016
U6  - https://doi.org/10.1134/S0037446616040030
SN  - 0037-4466
SN  - 1573-9260
VL  - 57
SP  - 589
EP  - 598
PB  - Pleiades Publ.
CY  - New York
ER  -