遗传QF-3⁺环
Hereditary QF-$3^{+}$ rings
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中文总结 AI 辅助
本文利用挠性理论方法，得到遗传QF-3⁺环的若干性质与刻画，证明其最大稳定子模根与内射包可交换，且存在到半单左/右阿廷环的双态射。
中文摘要 AI 辅助
借助挠性理论方法，本文得到了遗传QF-3⁺环的若干性质与刻画，这些刻画基于投射模范畴、内射投射模范畴以及Utumi定义的极大左/右商环。此外，证明了对于遗传QF-3⁺环，左/右模范畴上的“最大稳定子模”根与内射包可交换；还证明了这类环存在从其到半单左/右阿廷环的双态射（在带单位元的结合环范畴中）。
英文摘要
With the aid of the torsion-theoretical approach, several properties/characterizations of hereditary QF-$3^{+}$ rings are found. These characterizations are formulated in terms of the category of projective modules, the category of injective projective modules, and also in terms of the maximal left/right ring of quotients by Utumi. Moreover, it is shown that, for a hereditary QF-$3^{+}$ ring, the `largest stable submodule' radical (on the category of left/right modules) is permutable with injective envelopes. Besides, it is shown that there is a bimorphism (in the category of associative rings with identity) from such a ring to a semisimple left/right Artinian ring.
