The free -ring is a graded -ring.
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International Journal of Mathematics and Mathematical Sciences
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Warren, Roger D. (1993)
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We give some new characterizations of quasi-Frobenius rings by the generalized injectivity of rings. Some characterizations give affirmative answers to some open questions about quasi-Frobenius rings; and some characterizations improve some results on quasi-Frobenius rings.
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We characterize left Noetherian rings which have only trivial derivations.
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C0NTENTSIntroduction.................................................................................................................... 3§ 1. A subring theorem for free nilpotent Lie rings................................................. 10§ 2. The Lie ring associated with a free nilpotent group....................................... 20§ 3. Subrings which are associated with subgroups............................................ 27§ 4. Subgroups having the same Lie subring............................................................
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International Journal of Mathematics and Mathematical Sciences
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