A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is th...A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. 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.展开更多
文摘A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. 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.
