Computing free bases for projective modules

Bases for projective modules in An(k)

Let An(k) be the Weyl algebra, with k a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let M be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of M . If M is projective and rank(M) ≥ 2 we give a procedure to find a basis. © 2003 Elsevier Ltd. All righ...

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...

Projective modules over polynomial rings and dynamical Gröbner bases

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.

Computing Projective Indecomposable Modules and Higher Cohomology Groups

We describe the theory and implementation in Magma of algorithms to compute the projective indecomposable KG-modules for finite groups G and finite fields K. We describe also how they may be used together with dimension shifting techniques to compute cohomology groups Hn(G,M) for finite dimensional KG-modules M and n ≥ 3.