Polynomial functions on \Omega-groups.
by
Erhard Aichinger
Johannes Kepler Universtät Linz
Coauthors: Paweł M. Idziak (Jagiellonian University, Krakow, Poland)

We study the unary polynomial functions on a finite algebra A, where A is the expansion of a group (A, +, -, 0). In joint work with P.M.Idziak (based on his and K. S omczy\'nska's work on polynomially rich algebras), we have described when A is strictly 1-affine complete, i.e., when every partial unary congruence preserving operation can be interpolated by a polynomial function. The description is in terms of the congruence lattice of A, the commutator operation, and the size of certain subalgebras of homomorphic images of A.

We also see that polynomial functions on the direct product A₁ ×A₂ can be studied componentwise if and only if A₁ ×A₂ has no skew congruences.

Date received: May 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-24.