A CHARACTERIZATION OF BAER-IDEALS

• Main Author: Ali Taherifar
• Format: Article
• Language: English
• Published: Shahrood University of Technology 2014-09-01
• Series: Journal of Algebraic Systems
• Subjects: Quasi-Baer ring; Generalized right quasi-Baer; Semicentral idempotent; Spec(R); Extremally disconnected space
• Online Access: http://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdf
• ISSN: 2345-5128; 2345-511X

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer ideal is important. In this paper we investigate some properties of Baer-ideals and give a characterization of Baer-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular matrix rings, semiprime ring and ring of continuous functions. Finally, we find equivalent conditions for which the 2-by-2 generalized triangular matrix ring is right SA.