Rings whose class of projective modules is socle fine

On Projective Modules over Semi-hereditary Rings

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

The Euler class groups of polynomial rings and unimodular elements in projective modules

Let A be a commutative noetherian ring of dimension n. Let P be a projective A[T ]-module. Plumstead ([P]) proved that if rankP > dimA then P splits off a free summand of rank one. It is natural to ask what happens when rankP = dimA. In this paper we investigate this question when P has trivial determinant. Let α : P I be a generic surjection (i.e. I ⊂ A[T ] is an ideal of height n). It is prov...

ON PROJECTIVE L- MODULES

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

Complexes of $C$-projective modules

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

Projective modules over polynomial rings and dynamical Gröbner bases