论文标题
$ W $ - $ \ rm fp $ -projective模块和维度
$w$-$\rm FP$-projective modules and dimension
论文作者
论文摘要
令$ r $为戒指。当$ r $ -Module $ m $ $ $ $ $ $时，并且仅当$ \ ext^1_r（f，m）$是任何有限呈现的模块$ f $的GV-TORSION模块。在本文中，我们介绍并研究了$ W $ -FP-PROXTIVE模块的概念，该模块在某种程度上是$ \ rm fp $ -projective模块的概述。 $ r $ -Module $ m $据说为$ W $ - $ \ rm fp $ -projective，如果$ \ ext^1_r（m，n）= 0 $对于任何绝对$ w $ - pure-pure module $ n $。这类新的模块将用于表征（noetherian）$ dw $环。因此，我们介绍了$ w $ - $ \ rm fp $ -projective尺寸的模块和戒指。讨论了引入的维度与其他（经典）同源维度之间的关系。给出了说明性的例子。
Let $R$ be a ring. An $R$-module $M$ is said to be an absolutely $w$-pure module if and only if $\Ext^1_R(F,M)$ is a GV-torsion module for any finitely presented module $F$. In this paper, we introduce and study the concept of $w$-FP-projective module which is in some way a generalization of the notion of $\rm FP$-projective module. An $R$-module $M$ is said to be $w$-$\rm FP$-projective if $\Ext^1_R(M,N)=0$ for any absolutely $w$-pure module $N$. This new class of modules will be used to characterize (Noetherian) $DW$ rings. Hence, we introduce the $w$-$\rm FP$-projective dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. Illustrative examples are given.
