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

References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …

Drinfeld recently suggested to replace projective modules by the flat Mittag-Leffler ones in
the definition of an infinite dimensional vector bundle on a scheme X (Drinfeld, 2006 [8]) …

We study Mittag-Leffler conditions on modules providing relative versions of classical results
by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we …

The idea of purity pervades human culture, from religion through sexual and moral codes,
cleansing rituals and dietary rules, to stratifications of societies into castes. It does so to an …

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 …

Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and model
theory,[20],[14],[19]. If R is a non-right perfect ring, then it is known that in contrast with the …

In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …