Page 1 PURE AND APPLIED MATHEMATICS A Series of Monographs and Textbooks LINEAR
ALGEBRA OVER COMMUTATIVE RINGS Bernard R. McDonald Page 2 Linear Algebra Over …

Flat ideals II Page 1 manuscripta math. 22, 325 - 341 (1977) ~ by Springer-Verlag 1977 FLAT
IDEALS II Sarah Glaz and Wolmer V. Vasconcelos This paper is concerned with the …

0. Introduction. We begin here an inquiry into the nature of flat ideals in a commutative ring
A, with particular emphasis on questions of divisibility and finite generation As the main …

This paper is concerned with the problem of determining those integral domains D which
have the property that finitely generated projective modules over D [X,,..., X,] are extended …

The author and Ira J. Papick have termed an integral domain R a going-down ring if R⊂ T
satisfies going-down for each domain T containing R. The present paper investigates …

For a ring extension R ⊆ S,(R, S) is called a treed pair if every ring T, R ⊆ T ⊆ S, is treed.
When R is a field it is shown that the only treed pairs are those satisfying tr. deg S: R≤ 1. For …

In this paper, we study the class of rings in which every flat ideal is finitely generated. We
investigate the stability of this property under localization and homomorphic image, and its …

It is proved that if $ R $ is a $2 $-root closed two-dimensional going-down domain with no
factor domain of characteristic 2, then each integral overling of $ R $ is a going-down …

The property of a commutative ring A that finitely generated flat A-modules be projective is
known to be a property of the topology of Spec (A), the set of prime ideals of A| 10]. Similarly …

This paper is concerned with the relationship between $ R [X]/I $ being a projective $ R $-
module and $ I $ being a finitely generated ideal of $ R [X] $. It is shown that if $ R [X]/I $ is …