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Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167) by Alberto Facchini (auth.) is a nonfiction available to read on EtoBox.

What is Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167) about?

The purpose in writing this expository monograph has been three-fold. First, the author set out to present the solution of a problem posed by Wolfgang Krull in 1932. He asked whether what is now called the "Krull-Schmidt Theorem" holds for artinian modules. A negative answer was published only in 1995 by Facchini, Herbera, Levy and Vámos. Second, the author presents the answer to a question posed by Warfield in 1975, namely, whether the Krull-Schmidt-Theorem holds for serial modules. Facchini published a negative answer in 1996. The solution to the Warfield problem shows an interesting behavior; in fact, it is a phenomena so rare in the history of Krull-Schmidt type theorems that its presentation to a wider mathematical audience provides the third incentive for this monograph. Briefly, the Krull-Schmidt-Theorem holds for some, not all, classes of modules. When it does hold, any two indecomposable decompositions are uniquely determined up to one permutation. For serial modules the theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. Apart from these issues, the book addresses various topics in module theory and ring theory,

Who reads Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167)?

Author

Alberto Facchini (auth.)

Publisher

Birkhäuser Basel : Imprint: Birkhäuser

Published

1998

Language

EN

ISBN

9783034897693

Category

nonfiction

Subjects

Mathematics, Algebra, Stem