This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

Let R be an arbitrary ring. A nonzero unital right R-module M is called a second module if M
and all its nonzero homomorphic images have the same annihilator in R. It is proved that if R …

We define a dimension, called an FP-projective dimension, for modules and rings. It
measures how far away a finitely generated module is from being finitely presented, and …

Let R be a ring. A right R-module C is called cotorsion if for any flat right R-module biF. In
this paper, we first give some results on cotorsion envelopes that are analogous to those on …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

In this paper, we study generalized Reed-Solomon codes (GRS codes) over commutative
and noncommutative rings, we show that the classical Welch-Berlekamp and Guruswami …

This paper investigates situations where a property of a ring can be tested on a set of “prime
right ideals.” Generalizing theorems of Cohen and Kaplansky, we show that every right ideal …

Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

This textbook is designed for students with at least one solid semester of abstract algebra,
some linear algebra background, and no previous knowledge of module theory …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …