Certain basic functional identities of semiprime rings. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Lee, Tsiu-Kwen
• Is Part Of: Communications in algebra. Volume 47:Issue 1(2019)
• Page Start: 17
• Page End: 29
• Publication Date: 2019-01-02
• Subjects: (Semi)prime ring -- Posner's second theorem -- extended centroid -- orthogonal completion -- functional identity; 16R60 -- 16N60 -- 16W10 -- 16W25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1439049
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The goal of the article is to discuss certain basic functional identities of semiprime rings. Specifically, the following result is proved: Let R be a semiprime ring with extended centroid C and let f, g : R → Q m l ( R ) be additive maps, where Q m l ( R ) denotes the maximal left ring of quotients of R . Suppose that f ( x ) x + x g ( x ) ∈ C for all x ∈ R . Then there exist b ∈ Q m l ( R ), β ∈ C and additive maps ν, η : R → C such that f ( x ) = x b + ν ( x ) and g ( x ) = ( − b + β ) x + η ( x ) for all x ∈ R . Moreover, some related functional identities are also characterized.