论文标题
一个新的无限家族$σ$ - 质子戒指
A new infinite family of $σ$-elementary rings
论文作者
论文摘要
协会的封面（不一定是可交换或Unital）环$ r $是$ r $的适当子圈的集合，其设定理论的联盟等于$ r $。如果存在这样的盖子，则$ r $的覆盖号$σ（r）$是最小盖子的基础性，如果对于每个非零的两边$ i $ $ r $ $ $ r $ $ $ r $ $σ（r）<σ（r）<σ（r）<σ（r）<σ（r/i）$，则称为$σ$ - elementary。在本文中，我们提供了$σ$ - 元素环$ r $的第一个示例，这些$ r $具有非平凡的Jacobson Radical $ j $，$ r/j $ noncomputative，我们确定了这些环的覆盖号码。
A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$. If such a cover exists, then the covering number $σ(R)$ of $R$ is the cardinality of a minimal cover, and a ring $R$ is called $σ$-elementary if $σ(R) < σ(R/I)$ for every nonzero two-sided ideal $I$ of $R$. In this paper, we provide the first examples of $σ$-elementary rings $R$ that have nontrivial Jacobson radical $J$ with $R/J$ noncommutative, and we determine the covering numbers of these rings.
