Further Results on the Sharp Ordering in Rings. (25th October 2020) - Liu, Xiaoji; Fu, Shiqin; Yu, Yaoming
Abstract: In this article, we will present some results relating sharp ordering ( a ≤ ♯ b ) and investigate the properties of one-sided cyclic ideals in rings. Necessary and sufficient conditions for the invertibility and the group invertibility of the linear combination c 1 a + c 2 b are given, where a is below b under the sharp order, a and b are elements of an algebra, and c 1, c 2 are elements of an arbitrary field.