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A generalization of the Mitchell Lemma: The Ulmer Theorem and the Gabriel–Popescu Theorem revisited

2012; Elsevier BV; Volume: 216; Issue: 10 Linguagem: Inglês

10.1016/j.jpaa.2012.01.014

1873-1376

Septimiu Crivei, C. Năstăsescu, Laura Năstăsescu,

Rings, Modules, and Algebras

We prove a generalization of the Mitchell Lemma, and we show that it is a key lemma that can be used in order to deduce in a unified easier way several important results. Thus, the Ulmer Theorem, the generalized Gabriel–Popescu Theorem and the generalized Takeuchi Lemma are all consequences of the generalized Mitchell Lemma.