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Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules: 167 (Progress in Mathematics) - Hardcover
Inhaltsangabe
This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.
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"Written in an attractive and fresh mathematical style. Each topic is arranged well and lucidly. The author has made important contributions to the study of direct sum decompositions and many of the main results in this book include his own work."
--EMS Newsletter
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This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.
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Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167)
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Module Theory (Hardcover)
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Hardcover. Zustand: new. Hardcover. 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. Secondly, the author presents the answer to a question posed by Warfield in 1975, namely, whether the Krull-Schmidt Theorem holds for serial modules. The authors third incentive focuses on the fact that the Krull-Schmidt theorem holds for some, not all, classes of modules. Apart form these issues, the book addresses various topics in module theory and ring theory, some now considered classical and others more specialized. Open problems conclude the work. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9783764359089
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Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167)
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Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules (Progress in Mathematics, 167)
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Module Theory
Verlag:
Springer, Berlin, Springer, Basel Jun 1998, 1998
ISBN 10: 3764359080
ISBN 13: 9783764359089
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the 'Krull-Schmidt Theorem' holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the 'Krull-Schmidt Theorem' holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience. 288 pp. Englisch. Bestandsnummer des Verkäufers 9783764359089
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Module Theory
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Zustand: New. Addresses various topics in module theory and ring theory, some considered classical (such as Goldie dimension, semiperfect rings, Krull dimension, rings of quotients, and their applications) and others specialized (such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules, exchange property, -pure-injective modules). Series: Progress in Mathematics. Num Pages: 288 pages, biography. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 155 x 19. Weight in Grams: 660. . 1998. Hardback. . . . . Bestandsnummer des Verkäufers V9783764359089
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Module Theory
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Module Theory
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Module Theory
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Zustand: New. PRINT ON DEMAND pp. 285. Bestandsnummer des Verkäufers 18358201
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