GENERALIZATION OF SHORT MODULES

G. Bilhan

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GENERALIZATION OF SHORT MODULES

机译：短模块的广义化

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摘要

It is proved that, if R is a commutative local Noetherian ring, then an R-module M is (almost) short and coatomic if and only if it is Noetherian. Also, for a Dedekind Domain R and R-module M, M is (almost) short if and only if M is Noetherian or M contains a Noetherian submodule N such that M/N is (almost) short and is the injective hull of a simple R-module.

机译：证明了，如果R是交换性局部Noether环，则R-模M在（且仅当）是Noetherian时（几乎）短且是孤子的。同样，对于Dedekind域R和R-模块M，当且仅当M是Noetherian或M包含Noetherian子模块N时，M几乎是短的，使得M / N几乎是短的，并且是简单的R模块。

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来源
《Arabian Journal for Science and Engineering. Section A, Sciences》 |2007年第1a期|p.121-127|共7页
作者
G. Bilhan;
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作者单位

Dokuz Eylul Universitesi Fen-Edebiyat Fakultesi Matematik Bolumu Tmaztepe Yerleskesi 35160 Buca-Izmir-Turkey;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类自然科学总论;
关键词
mathematics; algebra; module theory;

机译：数学代数模块论;

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GENERALIZATION OF SHORT MODULES

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