Polynomial interpolation in expanded groups

Description

The unary polynomial functions on any algebra $\ab{A}$ are those functions that can be obtained from the identity function and the constant functions by using the fundamental operations of $\mathbf{A}$. Given an algebra $\mathbf{A}$, we try to determine which functions are polynomial. Only recently, P. Mayr and the speaker have determined the number of polynomial functions of certain linear groups. Often, one attempts to describe polynomial functions by preservation properties; for example, every polynomial function preserves congruences. For some algebras, this property actually characterizes polynomial functions. We will exhibit some results (by P. M. Idziak and the speaker) that describe those finite commutative rings with $1$ on which every congruence preserving function is polynomial.

Period	06 Nov 2004
Event title	2004 Southern Regional Weekend Algebra Conference
Event type	Conference
Location	United StatesShow on map