论文标题
$σ[m] $降低等级
Reduced rank in $σ[M]$
论文作者
论文摘要
使用Raggi et.al引入的Prime子模块的概念。我们将降低等级的概念扩展到模块理论上下文。我们研究了$σ[m] $ modulo的商类别。当$ m $ m $ $ m $是$ m $是半imemime goldie模块时，由$ m $ imbiontive hull cogogener cogogener cogogento。我们证明此商类别是光谱。稍后，我们考虑$σ[m] $ cogeners $ m $ imponive hull的遗传性扭转理论，其中$ \ mathfrak {l}（m）$是$ m $的主要自由基，我们在$ m $ $ m $的范围内表征了$ m $的主要范围。最后，我们在模块$ m $上提供条件，并带有内态环$ s $，以获取$ s $是Artininan戒指的订单，扩展了L.W.的显着定理。小的。
Using the concept of prime submodule introduced by Raggi et.al. we extend the notion of reduced rank to the module-theoretic context. We study the quotient category of $σ[M]$ modulo the hereditary torsion theory cogenerated by the $M$-injective hull of $M$ when $M$ is a semiprime Goldie module. We prove that this quotient category is spectral. Later we consider the hereditary torsion theory in $σ[M]$ cogenerated by the $M$-injective hull of $M/\mathfrak{L}(M)$ where $\mathfrak{L}(M)$ is the prime radical of $M$, and we characterize when the module of quotients of $M$, respect to this torsion theory, has finite length in the quotient category. At the end we give conditions on a module $M$ with endomorphism ring $S$ to get that $S$ is an order in an Artininan ring, extending a remarkable Theorem of L.W. Small.
