A CHARACTERIZATION OF BAER-IDEALS
Publish place: Journal of Algebraic Systems، Vol: 2، Issue: 1
Publish Year: 1393
Type: Journal paper
Language: English
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JR_JAS-2-1_003
Index date: 4 August 2015
A CHARACTERIZATION OF BAER-IDEALS abstract
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.
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