Invo-regular unital rings

Abstract

It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo–Khurana (Comm. Algebra, 2001), recently Nielsen and ˇSter showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017.

Authors and Affiliations

Peter Danchev

Keywords

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  • EP ID EP530443
  • DOI 10.17951/a.2018.72.1.45
  • Views 105
  • Downloads 0

How To Cite

Peter Danchev (2018). Invo-regular unital rings. Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica, 72(1), 45-53. https://europub.co.uk/articles/-A-530443