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http://dx.doi.org/10.4134/BKMS.b190642

ON S-EXCHANGE RINGS  

Liu, Dajun (School of Mathematics and Physics Anhui Polytechnic University)
Wei, Jiaqun (Institute of Mathematics School of Mathematics Sciences Nanjing Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 945-956 More about this Journal
Abstract
We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.
Keywords
Exchange rings; S-exchange rings; clean rings; weakly clean rings; ${\pi}$-regular rings;
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