Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

This expository monograph was written for three reasons. Firstly, we wanted to present the
solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we …

The themes of cancellation, internal cancellation, substitution and exchange have led to a lot
of interesting research in the theory of modules over commutative and noncommutative …

The main theme in classical ring theory is the structure theory of rings of a particular kind.
For example, no one text book in ring theory could miss the Wedderburn-Artin theorem …

Let R be an associative ring. This monograph deals with the right R-modules MR whose
endomorphism ring End (MR) is semilocal. More generally, let A be any preadditive …

Commutative monoids yield an analogy between the theory of factorization in commutative
integral domains and the theory of direct sum decompositions of modules. We show that the …

The aim of this introduction is to outline the general setting and to exhibit some examples, in
order to show interesting features of infinite length modules, but also to point out the …

By a careful investigation of the model theory of modules over a special class of uniserial
domains we give some (counter) examples to a decomposition of a serial module. For …

Let R be a semilocal ring, that is, R modulo its Jacobson radical J (R) is artinian. Then K0
(R/J (R)) is a partially ordered abelian group with order-unit, isomorphic to (Zn,≤, u) …

A ring S is said to have square stable range one (written ssr (S)= 1) if a S+ b S= S implies
that a 2+ bx is a unit for some x∈ S. In the commutative case, this extends the class of rings …