论文标题
指环相对于素基的对称性
Symmetricity of rings relative to the prime radical
论文作者
论文摘要
在本文中，我们介绍并研究了对称环的严格概括。我们称ring $ r \，\，\，'p-smmetric'$ IF对于任何$ a，\，b，\，c \，in r，\，abc = 0 $表示$ bac \ in p（r）$中，其中$ p（r）$是$ r $ $ r $的presitial of $ r $。结果表明，$ p $ - 平衡环的类位于中央对称环和广义弱对称环之间。 $ p $ - 符合戒指和其他一些已知类别的戒指之间提供了关系。从任意的$ p $ - 对称戒指中，我们产生了许多$ p $ - 符合戒指的家庭。
In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring $R \,\,\, 'P-symmetric'$ if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical of $R$. It is shown that the class of $P$-symmetric rings lies between the class of central symmetric rings and generalized weakly symmetric rings. Relations are provided between $P$-symmetric rings and some other known classes of rings. From an arbitrary $P$-symmetric ring, we produce many families of $P$-symmetric rings.
