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On JB-Rings

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Abstract

A ring R is a QB-ring provided that aR + bR = R with a, b ∈ R implies that there exists a y ∈ R such that \( a + by \in R^{{ - 1}}_{q} . \) It is said that a ring R is a JB-ring provided that R/J(R) is a QB-ring, where J(R) is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J(R)2.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410006, China

    Huanyin Chen*

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  1. Huanyin Chen*
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Correspondence to Huanyin Chen*.

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Chen*, H. On JB-Rings. Chin. Ann. Math. Ser. B 28, 617–628 (2007). https://doi.org/10.1007/s11401-007-0208-x

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  • DOI: https://doi.org/10.1007/s11401-007-0208-x

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