TY - JOUR
ID - 300
TI - A CHARACTERIZATION OF BAER-IDEALS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Taherifar, A.
AD - Department of Mathematics, Yasouj University, Yasouj, Iran.
Y1 - 2014
PY - 2014
VL - 2
IS - 1
SP - 37
EP - 51
KW - Quasi-Baer ring
KW - Generalized right quasi-Baer
KW - Semicentral idempotent
KW - Spec(R)
KW - Extremally disconnected space
DO - 10.22044/jas.2014.300
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_300.html
L1 - https://jas.shahroodut.ac.ir/article_300_2e4cb45d9d8d73d64020a61a5b0b5a76.pdf
ER -