Quasi-Baer Rings with Essential Prime Radicals |
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Authors: | Hai Lan Jin Jaekyung Doh |
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Institution: | 1. Department of Mathematics , Yanbian University , Yanji , China;2. Department of Mathematics , Busan National University , Busan , South Korea |
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Abstract: | A ring R is called “quasi-Baer” if the right annihilator of every right ideal is generated, as a right ideal, by an idempotent. It can be seen that a quasi-Baer ring cannot be a right essential extension of a nilpotent right ideal. Birkenmeier asked: Does there exist a quasi-Baer ring which is a right essential extension of its prime radical? We answer this question in the affirmative. Moreover, we provide an example of a quasi-Baer ring in which the right essentiality of the prime radical does not imply the left essentiality of the prime radical. |
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Keywords: | Column finite upper triangular matrix ring Generalized triangular matrix representation Quasi-Baer ring Triangulating dimension |
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