Some Notes on Relative Projective and Injective Dimensions

HE Dong-lin, LI Yu-yan

doi:10.13371/j.cnki.chin.q.j.m.2020.02.004

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 2: 171 - 178

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.02.004

Some Notes on Relative Projective and Injective Dimensions

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Department of Mathematics,Longnan Teachers College

HE Dong-lin(1983-), female, native of Baiyin, Gansu, M.S.D., Longnan Teachers College, engages in homological algebra; LI Yu-yan(1983-), male, native of Longnan, Gansu, M.S.D., Longnan Teachers College, engages in homological algebra.

Received date: 2020-03-10

Online published: 2020-11-10

Supported by

Supported by the 2019 Scientific Research Projects in Universities of Gansu Province(2019B-224)； the 2020 Gansu University Innovation Fund Projective (2020A-277)；

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Abstract

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 P_C-projective dimensions, and give a characterization when the inequality P_C-pd V max{P_C-pd U, P_C-pd W } is strict for an exact sequence 0 → U → V → W → 0. Dually, we study Π-self-orthogonal modules and I_C-injective dimensions, and give a similar characterization when the inequality I_C-id V max{I_C-idU, I_C-idW } is strict.

Key words： Hom-faithful; Hom-cofaithful; Σ-self-orthogonal; Π-self-orthogonal

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HE Dong-lin, LI Yu-yan . Some Notes on Relative Projective and Injective Dimensions[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(2) : 171 -178 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.004

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