Displaying similar documents to “Stably free, projective right ideals”

On the free character of the first Koszul homology module.

Antonio García Rodicio (1991)

Extracta Mathematicae

Similarity:

Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I. The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance: - (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H

When every flat ideal is projective

Fatima Cheniour, Najib Mahdou (2014)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper, we study the class of rings in which every flat ideal is projective. We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.