| 書目名稱 | Module Theory | | 副標(biāo)題 | Endomorphism rings a | | 編輯 | Alberto Facchini | | 視頻video | http://file.papertrans.cn/638/637931/637931.mp4 | | 概述 | Adds to the list of fundamental books on rings and modules.Develops the necessary background in a logical way.Joyful reading for algebraists ?.Includes supplementary material: | | 叢書名稱 | Modern Birkh?user Classics | | 圖書封面 |  | | 描述 | .The purpose of this expository monograph is three-fold. First, the solution of a problem posed by Wolfgang Krull in 1932 is presented. 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 answer to a question posed by Warfield in 1975, namely, whether the Krull-Schmidt-Theorem holds for serial modules, is described. 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, some now considered classical (such | | 出版日期 | Book 1998 | | 關(guān)鍵詞 | Artinian Modules; Krull-Schmidt-Theorem; Module Theory; Permutation; endomorphism ring; ring theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0303-8 | | isbn_softcover | 978-3-0348-0302-1 | | isbn_ebook | 978-3-0348-0303-8Series ISSN 2197-1803 Series E-ISSN 2197-1811 | | issn_series | 2197-1803 | | copyright | Springer Basel AG 1998 |
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