When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …

When every finitely generated flat module is projective Page 1 Journal of Algebra 277 (2004)
542–558 www.elsevier.com/locate/jalgebra When every finitely generated flat module is …

It is easy to see that every finitely generated module in a [M] is K-injective if and only if M is
semisimple (for in this case every cyclic module in a [M] is M-injective). In this paper we …

We study direct-sum decompositions of pure-projective modules over some classes of rings.
In particular, we determine several classes of rings over which every pure-projective left …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a
direct sum of countably generated modules [2, Theorem l]. If any direct summand A of a …

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a
direct sum of modules with local endomorphism rings if and only if every direct sum of copies …

We prove here, among other results, that if R is a commutative noetherian ring and
projective R [x 1,…, xn]-modules of rank⩽ Krull dim R are extended, then finitely generated …

We prove that, for every regular ring R, there exists an isomorphism between the monoids of
isomorphism classes of finitely generated projective right modules over the rings EndR (R …