论文标题
左Co-Köthe戒指及其特征
Left Co-Köthe Rings and Their Characterizations
论文作者
论文摘要
G.Köthe在1935年提出的经典问题要求描述环$ r $，以便每个左$ r $ $ module都是循环模块的直接总和（这些环被称为左基戒指）。 Köthe，Cohen和Kaplansky为所有交换戒指（是Artinian主要的理想环）解决了这个问题。在1962年至1965年期间，Kawada解决了Köthe的基本fnite维代数的问题。但是，到目前为止，在非交互环境中，科思的问题已经开放。 Recently, in the paper ["Several characterizations of left Köthe rings", submitted], we classified left Köthe rings into three classes one contained in the other: left Köthe rings, strongly left Köthe rings and very strongly left Köthe rings, and then, we solved Köthe's problem by giving several characterizations of these rings in terms of describing the indecomposable modules.在本文中，我们将介绍这些概念的莫里塔二，左Co-Köthe环，强烈的左Co-Köthe环和非常强烈的左Co-KötheRings，然后为每个人提供了几个结构性特征。
Köthe's classical problem posed by G. Köthe in 1935 asks to describe the rings $R$ such that every left $R$-module is a direct sum of cyclic modules (these rings are known as left Köthe rings). Köthe, Cohen and Kaplansky solved this problem for all commutative rings (that are Artinian principal ideal rings). During the years 1962 to 1965, Kawada solved Köthe's problem for basic fnite-dimensional algebras. But, so far, Köthe's problem was open in the non-commutative setting. Recently, in the paper ["Several characterizations of left Köthe rings", submitted], we classified left Köthe rings into three classes one contained in the other: left Köthe rings, strongly left Köthe rings and very strongly left Köthe rings, and then, we solved Köthe's problem by giving several characterizations of these rings in terms of describing the indecomposable modules. In this paper, we will introduce the Morita duals of these notions as left co-Köthe ring, strongly left co-Köthe rings and very strongly left co-Köthe rings, and then, we give several structural characterizations for each of them.
