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Quasiunit regularity and QB-rings

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Ukrainian Mathematical Journal Aims and scope

Some relations for quasiunit regular rings and QB-rings, as well as for pseudounit regular rings and QB ∞-rings, are obtained. In the first part of the paper, we prove that (an exchange ring R is a QB-ring) ⟺ (whenever x ∈ R is regular, there exists a quasiunit regular element w ∈ R such that x = xyx = xyw for some y ∈ R) ⟺ (whenever aR + bR = dR in R; there exists a quasiunit regular element w ∈ R such that a + bz = dw for some z ∈ R). Similarly, we also give necessary and sufficient conditions for QB ∞-rings in the second part of the paper.

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Authors and Affiliations

  1. School of Science, Xi’an University of Technology, Xi’an, China

    Xiaoqing Sun, Shangping Wang, Xiaoqin Shen & Jianghua Li

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  1. Xiaoqing Sun
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  2. Shangping Wang
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  3. Xiaoqin Shen
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  4. Jianghua Li
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 415–425, March, 2012.

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Sun, X., Wang, S., Shen, X. et al. Quasiunit regularity and QB-rings. Ukr Math J 64, 470–483 (2012). https://doi.org/10.1007/s11253-012-0659-4

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  • DOI: https://doi.org/10.1007/s11253-012-0659-4

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