%0 Journal Article
%T A CHARACTERIZATION OF BAER-IDEALS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Taherifar, A.
%D 2014
%\ 09/01/2014
%V 2
%N 1
%P 37-51
%! A CHARACTERIZATION OF BAER-IDEALS
%K Quasi-Baer ring
%K Generalized right quasi-Baer
%K Semicentral idempotent
%K Spec(R)
%K Extremally disconnected space
%R 10.22044/jas.2014.300
%X 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.
%U https://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdf