Faithfully projective modules and clean algebras | CiNii Research CiNii 国立情報学研究所 学術
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Let R be a commutative ring with identity. A short exact sequence E of R-modules is said to
be neat (respectively, P-pure) if the sequence Hom R (S, E)(respectively, S⊗ RE) is exact for …

The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …

Fieldhouse observed that any finitely presented left R-module P is projective with respect to
pure exact sequences, ie can always be completed to a commutative diagram when the …

As a natural generalization of the classical theory of simple algebras, Au&rider and Goldman
established the theory of separable algebras in [I]. They proved in particular that if/l is a …

Given a commutative ring R, a finitely generated augmented R-algebra A is projective over
R if there is a finitely generated augmented R-algebra B such that the tensor product of A …

In previous articles we have discussed integrality and its relation to the spectra. In this paper
we wish to single out those algebras which would in the classical commutative case …

Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …

We make a detailed study of idempotent ideals that are traces of countably generated
projective right modules. We associate to such ideals an ascending chain of finitely …

Absolutely pure modules act in ways similar to injective modules. There are conditions on a
ring which guarantee that the class of injective modules will be covering. In this article, we …