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Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
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Lattice Concepts of Module Theory (Hardcover, 2000 ed.)
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Lattice Concepts of Module Theory (Hardcover, 2000 ed.)
Series: Texts in the Mathematical Sciences, 22
Expected to ship within 10 - 15 working days
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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.
General
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