In this paper, we study interplay between exchange ring R and their J-semisimple
indecomposable factor rings. In particular, we prove that for any (exchange) ring R and any …

This paper studies finitely generated projective modules over exchange rings. We prove that
cancellation holds in p (R), and K o (R) is completely determined by the continuous maps …

A separative ring is one whose finitely generated projective modules satisfy the property A⊕
A⋟ A⊕ B⋟ B⊕ B⇒ A⋟ B. This condition is shown to provide a key to a number of …

F-rings need not be ∏-homogeneous Page 1 COMMUNICATIONS IN ALGEBRA, 17(6),
1495-1504 (1989) F-RINGS NEED NOT BE n-HOMOGENEOUS Gene D. Abrams University of …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

All rings are assumed to be associative and with nonzero identity element. Unless otherwise
stated all modules are unital right modules. Expressions such as “a Noetherian ring” mean …

Publisher Summary This chapter discusses the modules, along with the exchange property
and exchange rings. All rings are assumed to be associative and unital. If A is a ring, then J …

In the present paper, we give a more explicite criterion of the directly finiteness of projective
modules over each types and show the following for a df regular ring R satisfying the c …

We characterize when the direct sum of an extending module and an injective module is
extending and when the direct sum of an extending module with the finite exchange property …

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 …