A note on the right-left symmetry of a R b R = (a + b) R in rings

TSIU-KWEN LEE2021-07-212021-07-2120212194988https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103888242&doi=10.1142%2fS0219498822501456&partnerID=40&md5=61d6022609a96213736db51222760c60https://scholars.lib.ntu.edu.tw/handle/123456789/572144We give an example to show that, for nonunital rings R, the direct sum aR ± bR = (a + b)R with a + b regular has no in general right-left symmetry. It is then proved that the right-left symmetry actually holds in a left and right faithful ring. ? 2022 World Scientific Publishing Company.[SDGs]SDG10A note on the right-left symmetry of a R b R = (a + b) R in ringsjournal article10.1142/S02194988225014562-s2.0-85103888242