We consider the question of how minimal acyclic complexes of finitely generated free
modules arise over a commutative local ring. A standard construction gives that every totally …

We identify a large class of rings over which locally free modules are determined by their
endomorphism rings. We characterize these endomorphism rings and consider under what …

Pierce [3] has shown that over a commutative regular ring every finitely generated
submodule of an n-generated module is n-generated, and then has asked if this result holds …

We study associative rings with a unit and unitary modules. Lazard stated in [I, p. 440] a
conjecture that if a quotient module po/~(pu) of a projective module p0 modulo its radical J …

RINGS WHOSE MODULES ARE WEAKLY SUPPLEMENTED ARE PERFECT. APPLICATIONS
TO CERTAIN RING EXTENSIONS Page 1 MATH. SC AND. 105 (2009), 25-30 RINGS WHOSE …

This paper studies infinite acyclic complexes of finitely generated free modules over a
commutative noetherian local ring $(R,\fm) $ with $\fm^ 3= 0$. Conclusive results are …

A module M is called continuous if (i) every submodule of M is essential in a summand of M,
and (ii) if a submodule A is isomorphic to a summand of M, then A is itself a summand of M …

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 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 …

A module M over a ring A is said to be stably free if M© F is a free A-module for some finitely
generated free A-module F. Clearly free A-modules are stably free. The converse is false in …