书目名称 | Serial Rings | 编辑 | Gennadi Puninski | 视频video | http://file.papertrans.cn/866/865425/865425.mp4 | 图书封面 |  | 描述 | The main theme in classical ring theory is the structure theory of rings of a particular kind. For example, no one text book in ring theory could miss the Wedderburn-Artin theorem, which says that a ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of full matrix rings over skew fields. This is an example of a finiteness condition which, at least historically, has dominated in ring theory. Ifwe would like to consider a requirement of a lattice-theoretical type, other than being Artinian or Noetherian, the most natural is uni-seriality. Here a module M is called uni-serial if its lattice of submodules is a chain, and a ring R is uni-serial if both RR and RR are uni-serial modules. The class of uni-serial rings includes commutative valuation rings and closed under homomorphic images. But it is not closed under direct sums nor with respect to Morita equivalence: a matrix ring over a uni-serial ring is not uni-serial. There is a class of rings which is very close to uni-serial but closed under the constructions just mentioned: serial rings. A ring R is called serial if RR and RR is a direct sum (necessarily finite) of uni-serial modules. Amongst others this class | 出版日期 | Book 2001 | 关键词 | Finite; Morphism; algebra; commutative property; endomorphism ring; model theory; ring theory | 版次 | 1 | doi | https://doi.org/10.1007/978-94-010-0652-1 | isbn_softcover | 978-94-010-3862-1 | isbn_ebook | 978-94-010-0652-1 | copyright | Springer Science+Business Media Dordrecht 2001 |
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