论文标题
在非交通戒指中几乎质量和正确的$ s $ prime理想的概括
Generalizations of almost prime and right $S$-prime ideals in noncommutative rings
论文作者
论文摘要
令$ r $为非交换戒指，让$ s $为$ r $的$ M $ $系统。在本文中，我们就几乎素数（右）理想的概念给出了更多结果，这些概念是由前两位作者引入的，尤其是在（右）$ s $ - 联合戒指，本地戒指和可分解的戒指中。此外，我们介绍了几乎正确的$ s $ prime理想的概念，并展示了如何将一些关于几乎主要理想的发现作为几乎正确的$ s $ $ prime理想的后果。此外，我们还展示了几乎正确的$ s $ prime理想在相关环中的表现，例如同构图像，商戒指和可分解的戒指。最后，我们使用Nagata理想化方法构建了几乎正确的$ S $ prime理想。
Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by the first two authors, especially in (right) $S$-unital rings, local rings, and decomposable rings. In addition, we introduce the concept of almost right $S$-prime ideals, and we show how some findings regarding almost prime ideals can be derived as consequences of almost right $S$-prime ideals. Besides, we show how almost right $S$-prime ideals behave in related rings such as homomorphic images, quotient rings, and decomposable rings. Finally, we construct almost right $S$-prime ideals using the Nagata method of idealization.
