Further Results on the Sharp Ordering in Rings. (25th October 2020)

• Record Type: Journal Article
• Authors: Liu, Xiaoji; Fu, Shiqin; Yu, Yaoming
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 14(2020)
• Page Start: 1704
• Page End: 1716
• Publication Date: 2020-10-25
• Subjects: Group inverse -- Moore–Penrose inverse -- reverse order -- sharp ordering; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1740931
• Languages: English
• ISSNs: 0163-0563

Abstract

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.