论文标题
在分级的S-Prime子模块上
On Graded s-Prime Submodules
论文作者
论文摘要
在本文中，我们介绍了分级$ s $ prime子模型的概念，这是分级prime子模型的概括。我们研究了这个概念在分级同态，分级模块的定位，直接产物和理想化方面的行为。我们成功地证明了在分级的noetherian模块的情况下，分级$ s $ prime子模块的存在。此外，我们为在一般情况下存在此类对象的存在提供了一些足够的条件，以及在特定的情况下，有限的组或一个polycyclic-by-finite组对$ \ mathbb {z} $进行评分。
In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules, direct product, and idealization. We succeeded to prove the existence of graded $s$-prime submodules in the case of graded-Noetherian modules. Also, we provide some sufficient conditions for the existence of such objects in the general case, as well as, in the particular case of grading by $\mathbb{Z}$, a finite group, or a polycyclic-by-finite group, in addition to crossed product grading.
