Commutative rings with finite quotient fields

TL;DR

This paper characterizes a class of commutative reduced rings with a finite subset ensuring surjective projections on prime ideal quotients, providing a complete structure theorem and exploring related finiteness conditions.

Contribution

It introduces a new class of rings defined by a finite subset with surjective projections, and offers a comprehensive structure theorem for these rings.

Findings

Complete structure theorem for the class of rings

Relation with other finiteness conditions on quotients

Characterization of rings with finite quotient fields

Abstract

We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals.