An Equivalent Condition and Some Properties of Strong J-Symmetric Ring

Shun Xu and Qingkai Zhao

Journal of Mathematics, 2021, vol. 2021, 1-6

Abstract: Let JR denote the Jacobson radical of a ring R. We say that ring R is strong J-symmetric if, for any a,b,c∈R, abc∈JR implies bac∈JR. If ring R is strong J-symmetric, then it is proved that Rx/xn is strong J-symmetric for any n≥2. If R and S are rings and WSR is a R,S-bimodule, E=TR,S,W=RW0S=rw0s|r∈R,w∈W,s∈S,then it is proved that R and S are J-symmetric if and only if E is J-symmetric. It is also proved that R and S are strong J-symmetric if and only if E is strong J-symmetric.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7335202

DOI: 10.1155/2021/7335202

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