论文标题
在二人组，可逆和对称群环上
On Duo, Reversible and Symmetric Group Rings
论文作者
论文摘要
让$ rg $表示带有身份的扭转组$ g $ $ g $的组环。在本文中，我们介绍了一些在文献中似乎没有证明的陈述的证据。我们在组环的环境中建立了环理论条件二重奏，可逆，SI属性和对称性之间的有效含义。我们进一步表明，如果Group Ring $ RG $拥有这些物业中的任何一个，那么$ G $是Hamiltonian集团，$ R $的特征是$ 0 $或$ 2 $。此外，在以下情况下，我们表征了组环$ rg $中相同的属性：（$ 1）$ $ $ rg $是半简单组戒指，（$ 2 $）$ r $是一个半简单的戒指和$ g $任何组。
Let $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications between the ring-theoretic conditions duo, reversible, SI property and symmetric in the setting of group rings. We further show that if the group ring $RG$ possesses any of these properties, then $G$ is a Hamiltonian group and the characteristic of $R$ is either $0$ or $2$. Moreover, we characterize the same properties in group rings $RG$ in the following cases: ($1)$ $RG$ is a semi-simple group ring and ($2$) $R$ is a semi-simple ring and $G$ any group.
