Gorenstein projective dimension relative to a semidualizing bimodule. (English) Zbl 1287.16015
This paper investigates the properties of \(G_c\)-projective modules and the \(G_c\)-projective dimension of modules over general rings. The obtained results are interesting.
Reviewer: Zhan Jianming (Enshi)
MSC:
16E10 | Homological dimension in associative algebras |
16E05 | Syzygies, resolutions, complexes in associative algebras |
18G25 | Relative homological algebra, projective classes (category-theoretic aspects) |
18G20 | Homological dimension (category-theoretic aspects) |
Keywords:
Gorenstein projective dimension; semidualizing bimodules; Auslander classes; Foxby equivalence; Bass classes; projective modulesReferences:
[1] | DOI: 10.1112/S0024611502013527 · Zbl 1047.16002 · doi:10.1112/S0024611502013527 |
[2] | Auslander , M. , Bridger , M. ( 1969 ). Stable module theory.Memoirs Amer. Math. Soc.Vol. 94. Providence, RI: Amer. Math. Soc. · Zbl 0204.36402 |
[3] | Christensen L. W., Noetherian and Non-Noetherian Perspectives pp 101– (2011) |
[4] | DOI: 10.1016/j.jalgebra.2005.12.007 · Zbl 1104.13008 · doi:10.1016/j.jalgebra.2005.12.007 |
[5] | Christensen L. W., J. Pure Appl. Algebra 208 pp 177– (2007) · Zbl 1105.13014 · doi:10.1016/j.jpaa.2005.12.005 |
[6] | DOI: 10.1007/BF02760849 · Zbl 0464.16019 · doi:10.1007/BF02760849 |
[7] | DOI: 10.1007/BF02572634 · Zbl 0845.16005 · doi:10.1007/BF02572634 |
[8] | DOI: 10.1515/9783110803662 · doi:10.1515/9783110803662 |
[9] | DOI: 10.1016/j.jalgebra.2010.09.040 · Zbl 1216.18015 · doi:10.1016/j.jalgebra.2010.09.040 |
[10] | DOI: 10.1016/j.jpaa.2003.11.007 · Zbl 1050.16003 · doi:10.1016/j.jpaa.2003.11.007 |
[11] | DOI: 10.1016/j.jpaa.2005.07.010 · Zbl 1094.13021 · doi:10.1016/j.jpaa.2005.07.010 |
[12] | Holm H., J. Math. Kyoto Univ. 47 pp 781– (2007) |
[13] | Iwanaga Y., Tsukuba J. Math. 4 pp 107– (1980) |
[14] | Sather-Wagstaff S., J. London Math. Soc. 77 pp 481– (2008) · Zbl 1140.18010 · doi:10.1112/jlms/jdm124 |
[15] | DOI: 10.1016/j.jalgebra.2010.07.007 · Zbl 1207.13009 · doi:10.1016/j.jalgebra.2010.07.007 |
[16] | Takahashi R., Math. Scand. 106 pp 5– (2010) · Zbl 1193.13012 · doi:10.7146/math.scand.a-15121 |
[17] | DOI: 10.1216/JCA-2010-2-1-111 · Zbl 1237.13029 · doi:10.1216/JCA-2010-2-1-111 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.