A CHARACTERIZATION OF BAER-IDEALS

An ideal I of a ring R is called a right Baer-ideal if there exists an idempotent e € 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? R the ideal I? is a right Baer-ideal, and R is right principaly quasi-Baer if every prin- cipal right ideal of R is a right Baer-ideal. Therefore the concept of Baer ideal is important. In this paper we investigate some prop- erties of Baer-ideals and give a characterization of Baer-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangu-lar matrix rings, semiprime ring and ring of continuous functions. Finally, we nd equivalent conditions for which the 2-by-2 gener- alized triangular matrix ring be right SA.

Keywords:

Quasi-Baer ring , Generalized right quasi-Baer , Semicentral idempotent , Spec(R) , Extremally disconnected space