Lattice Concepts of Module Theory is popular PDF and ePub book, written by Grigore Calugareanu in 2013-04-17, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lattice Concepts of Module Theory can be Read Online from any device for your convenience.
Lattice Concepts of Module Theory Book PDF Summary
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.
Detail Book of Lattice Concepts of Module Theory PDF
- Author : Grigore Calugareanu
- Release : 17 April 2013
- Publisher : Springer Science & Business Media
- ISBN : 9789401595889
- Genre : Mathematics
- Total Page : 233 pages
- Language : English
- PDF File Size : 19,5 Mb
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