A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

In this paper, we discuss the Bass class and the Auslander class with respect to a
semidualizing module over an associative ring. Let _SC_R be a semidualizing module, we …

Let R be a commutative ring with prime nilradical Nil (R) and M an R-module. Define the
map 𝜙: R→ R Nil (R) by ${\phi}(r)=\frac {r}{1} $ for r∈ R and 𝜓: M→ M Nil (R) by …

Given modules X and Y, X is said to be Y-subprojective if for every epimorphism\(\pi:
P\rightarrow Y\) and every homomorphism\(\alpha: X\rightarrow Y\), there exists a …

Abstract Given modules $ A_ {R} $ and $ _ {R} B $, $ _ {R} B $ is called absolutely $ A_ {R}
$-pure if for every extension $ _ {R} C $ of $ _ {R} B $, $ A\otimes B\rightarrow A\otimes C …

Let S and R be rings, SCR a (faithfully) semidualizing bi-module, and n 1 a natural number.
In this paper, we introduce the concepts of C-fpn-injective and C-fpn-at modules. Then we …

Injective and Projective Properties of <Emphasis Type="Italic">R</Emphasis>[<Emphasis
Type="Italic Page 1 Czechoslovak Mathematical Journal, 54 (129) (2004), 573–578 INJECTIVE …

Rad-injective and Almost-injective Modules and Rings Page 1 Algebra Colloquium c© 2011
AMSS CAS & SUZHOU UNIV Algebra Colloquium 18 : 3 (2011) 411–418 Rad-injective and …

A ring R is said to be left n-semihereditary, if every n-generated left ideal of R is projective. It
is shown that for a ring R, the following statements are equivalent:(1) R is left n …

We investigate modules M having the injective property relative to nonsingular modules.
Such modules are called “N-injective modules”. It is shown that M is an N-injective R-module …