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

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  • Shun Xu
  • Qingkai Zhao

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.

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  • Shun Xu & Qingkai Zhao, 2021. "An Equivalent Condition and Some Properties of Strong J-Symmetric Ring," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, September.
    • Handle: RePEc:hin:jjmath:7335202
    DOI: 10.1155/2021/7335202
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