Texts in the Mathematical Sciences

Lattice Concepts of Module Theory

Authors: Calugareanu, Grigore

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About this book

It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc­ ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists". Indeed, many module-theoretic results can be proved by using lattice theory alone. The purpose of this book is to collect and present all and only the results of this kind, although for this purpose one must develop some significant lattice theory. The results in this book are of the following categories: the folklore of Lattice Theory (to be found in each Lattice Theory book), module­ theoretic results generalized in (modular, and possibly compactly gen­ erated) lattices (to be found in some 6 to 7 books published in the last 20 years), very special module-theoretic results generalized in lattices (e. g. , purity in Chapter 9 and several dimensions in Chapter 13, to be found mostly in [27], respectively, [34] and [18]) and some new con­ cepts (e. g.

Table of contents (14 chapters)

  • Basic notions and results

    Călugăreanu, Grigore

    Pages 1-16

  • Compactly generated lattices

    Călugăreanu, Grigore

    Pages 17-27

  • Composition series. Decompositions

    Călugăreanu, Grigore

    Pages 29-38

  • Essential elements. Pseudo—complements

    Călugăreanu, Grigore

    Pages 39-45

  • Socle. Torsion lattices

    Călugăreanu, Grigore

    Pages 47-58

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-94-015-9588-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-0-7923-6488-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-90-481-5530-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lattice Concepts of Module Theory
Authors
Series Title
Texts in the Mathematical Sciences
Series Volume
22
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-9588-9
DOI
10.1007/978-94-015-9588-9
Hardcover ISBN
978-0-7923-6488-7
Softcover ISBN
978-90-481-5530-9
Series ISSN
0927-4529
Edition Number
1
Number of Pages
XIII, 225
Topics