Lattice concepts of module theory. (English) Zbl 0959.06001

Călugăreanu, Grigore

Kluwer Texts in the Mathematical Sciences. 22. Dordrecht: Kluwer Academic Publishers. xiii, 225 p. (2000).

The monograph is meant as a textbook for graduate students and researchers whose work involves orders, lattices, group theory and generalizations, general module theory, and rings and algebras. There are four principal topics in the book, namely basic properties of lattices, module-theoretic results generalized in lattices (modules and compactly generated lattices), very special module-theoretic results generalized in lattices (purity and several dimensions) and some new concepts introduced in lattices by the author (fully invariant elements, CS (or extending) and FI-extending lattices). The content is divided into 14 chapters, each of which contains several exercises, the solutions of which are collected in the last extensive one (this chapter has 53 pages).

Reviewer: Ladislav Bican (Praha)

MSC:

06-02	Research exposition (monographs, survey articles) pertaining to ordered structures
16-02	Research exposition (monographs, survey articles) pertaining to associative rings and algebras
13-02	Research exposition (monographs, survey articles) pertaining to commutative algebra
06B99	Lattices

Keywords:

order; lattice; group; ring; module; algebra; textbook