数学季刊 ›› 2020, Vol. 35 ›› Issue (2): 171-178.doi: 10.13371/j.cnki.chin.q.j.m.2020.02.004
摘要: Let R be an associative(not necessary commutative) ring. In this paper,we give some properties of Hom-faithful and Hom-cofaithful R-modules. We investigate Σ-self-orthogonal R-modules and PC-projective dimensions, and give a characterization when the inequality PC-pd V max{PC-pd U, PC-pd W } is strict for an exact sequence 0 → U → V → W → 0. Dually, we study Π-self-orthogonal modules and IC-injective dimensions, and give a similar characterization when the inequality IC-id V max{IC-idU, IC-idW } is strict.
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