Affiliation:
1. Stat-Math Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, West Bengal, India
Abstract
If [Formula: see text] is a finite commutative ring, it is well known that there exists a nonzero polynomial in [Formula: see text] which is satisfied by every element of [Formula: see text]. In this paper, we classify all commutative rings [Formula: see text] such that every element of [Formula: see text] satisfies a particular monic polynomial. If the polynomial, satisfied by the elements of [Formula: see text], is not required to be monic, then we can give a classification only for Noetherian rings, giving examples to show that the characterization does not extend to arbitrary commutative rings.
Funder
National Board for Higher Mathematics
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory