| 書目名稱 | Module Theory | | 副標(biāo)題 | Endomorphism rings a | | 編輯 | Alberto Facchini | | 視頻video | http://file.papertrans.cn/638/637930/637930.mp4 | | 叢書名稱 | Progress in Mathematics | | 圖書封面 |  | | 描述 | 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 | | 出版日期 | Book 1998 | | 關(guān)鍵詞 | modules; ring theory; endomorphism ring; Lattice; matrices; Permutation; ring | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8774-8 | | isbn_ebook | 978-3-0348-8774-8Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel AG 1998 |
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