论文标题
$ \ aleph_0 $ - 分布式模块和戒指
$\aleph_0$-distributive modules and rings
论文作者
论文摘要
让$ a $是原理理想最低条件的戒指。事实证明，$ \ aleph_0 $ -distribnite右（左）$ a $ modules与Artinian（Noetherian）右（左）$ a $ a $ modules一致。戒指，在其上，所有正确的模块是$ \ aleph_0 $ - 分发与有限表示类型的戒指的直接总和。圆环的右模块是半分布，与川田环相吻合，其基础环完全循环。图甘巴夫的研究得到了俄罗斯科学基金会的支持，项目22-11-00052。
Let $A$ be a ring with minimum condition on principal right ideals. It is proved that $\aleph_0$-distributive right (left) $A$-modules coincide with Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right modules are direct sums of $\aleph_0$-distributive coincide with rings of of finite representation type. Rings, whose right modules are semidistributive, coincide with Kawada rings, over basis rings of which all right modules are completely cyclic. The studies of Tuganbaev are supported by Russian Scientific Foundation, project 22-11-00052.
