WEAKLY CONTINUOUS AND C2-RINGS |
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Abstract: | A ring R is called right weakly continuous if the right annihilator of each element is essential in a summand of R, and R satisfies the right C2-condition (every right ideal that is isomorphic to a direct summand of R is itself a direct summand). We show that a ring R is right weakly continuous if and only if it is semiregular and J(R) = Z(R R ). Unlike right continuous rings, these right weakly continuous rings form a Morita invariant class. The rings satisfying the right C2-condition are studied and used to investigate two conjectures about strongly right Johns rings and right FGF-rings and their relation to quasi-Frobenius rings. |
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Keywords: | Semiregular rings Continuous rings C2-condition FGF-rings Quasi-Frobenius rings Johns rings 1991 Subject Classification: 16D50, 16L60, 16E50 |
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