A note on algebraic extensions modulo I

Abstract

Let I be a nonzero ideal of a ring T , let ' W T ! E WD T =I denote the canonical projection, let D be a ring contained in E, and let R D ' 1 .D/. The main purpose of this paper is to characterize when the ring extension R T is n-(resp., universally) algebraic modulo I in case I is an intersection of finitely many maximal ideals of T .