G_C-projectivity and injectivity under Frobenius extensions

References

• Auslander, M., Bridger, M. (1969). Stable Module Theory, Memoirs of the Amer. Math. Soc. Vol. 94. Providence, R.I.: American Mathematical Society.
   Google Scholar
• Bennis, D., Mahdou, N. (2009). Global Gorenstein dimensions. Proc. Amer. Math. Soc. 138(02):461–465. DOI: 10.1090/S0002-9939-09-10099-0.
   Google Scholar
• Chen, X. W. (2008). An Auslander-type result for Gorenstein-projective modules. Adv. Math. 218(6):2043–2050. DOI: 10.1016/j.aim.2008.04.004.
   Web of Science ®Google Scholar
• Christensen, L. W. (2000). Gorenstein Dimenensions, Lecture Notes in Math., Vol. 1747. Berlin: Springer-Verlag.
   Google Scholar
• Enochs, E. E., Jenda, O. M. G. (1995). Gorenstein injective and projective modules. Math. Z. 220(1):611–633. DOI: 10.1007/BF02572634.
   Web of Science ®Google Scholar
• Fischman, D., Montgomery, S., Schneider, H.-J. (1997). Frobenius extensions of subalgebras of Hopf algebras. Trans. Amer. Math. Soc. 349(12):4857–4895. DOI: 10.1090/S0002-9947-97-01814-X.
   Web of Science ®Google Scholar
• Foxby, H. B. (1972). Gorenstein modules and related modules. Math. Scand. 31:267–284. DOI: 10.7146/math.scand.a-11434.
   Web of Science ®Google Scholar
• Golod, E. S. (1984). G-dimension and generalized perfect ideals. Trudy Mat. Inst. Steklov. 165:62–66. Algebraic geometry and its applications.
   Google Scholar
• Holm, H. (2004). Gorenstein homological dimensions. J. Pure Appl. Algebra 189(1-3):167–193. DOI: 10.1016/j.jpaa.2003.11.007.
   Web of Science ®Google Scholar
• Holm, H., Jørgensen, P. (2006). Semidualizing modules and related Gorenstein homological dimensions. J. Pure Appl. Algebra 205(2):423–445. DOI: 10.1016/j.jpaa.2005.07.010.
   Web of Science ®Google Scholar
• Huang, C. L. (2012). GC-projective, injective and flat modules under change of rings. J. Algebra Appl. 11:1–16.
   Web of Science ®Google Scholar
• Huang, Z. Y., Sun, J. X. (2012). Invariant properties of represenations under excellent extensions. J. Algebra 358:87–101. DOI: 10.1016/j.jalgebra.2012.03.004.
   Web of Science ®Google Scholar
• Kadison, L. (1996). The jones polynomial and certain separable Frobenius extensions. J. Algebra 186(2):461–475. DOI: 10.1006/jabr.1996.0383.
   Web of Science ®Google Scholar
• Kadison, L. (1999). New Examples of Frobenius Extensions, University Lecture Series, Vol 14, Provedence, RI: AMS.
   Google Scholar
• Kasch, F. (1954). Grundlagen einer theorie der Frobenius-Erweiterungen. Math. Ann. 127(1):453–474. DOI: 10.1007/BF01361137.
   Google Scholar
• Liu, Z. F., Huang, Z. Y., Xu, A. M. (2013). Gorenstein projective dimension relative to a semidualizing bimodule. Commun. Algebra 41(1):1–18. DOI: 10.1080/00927872.2011.602782.
   Web of Science ®Google Scholar
• Morita, K. (1965). Adojint pairs of functors and Frobenius extension. Sci. Rep. Toyko Kyoiku Daigaku (Sect. A) 9:40–71.
   Google Scholar
• Nakayama, T., Tsuzuku, T., On Frobenius extension I, Nagoya Math. J. 17 (1960) 89–110; On Frobenius extensions II, Nagoya Math J. 19(1961):127–148. DOI: 10.1017/S0027763000002075.
   Google Scholar
• Ren, W. (2008). Gorenstein projective and injective dimensions over Frobenius extensions. Commun. Algebra 46:1–7.
   Google Scholar
• Schneider, H.-J. (1992). Normal basis and transitivity of crossed products for Hopf algebras. J. Algebra 152(2):289–312. DOI: 10.1016/0021-8693(92)90034-J.
   Web of Science ®Google Scholar
• Vasconcelos, W. V. (1974). , Divisor Theory in Module Categories, North-Holland Mathematics Studies, No.14, Notes on Mathematics, No. 53. Amsterdam: North-Holland Publishing Co.
   Google Scholar
• White, D. (2010). Gorenstein projective dimension with respect to a semidualizing module. J. Comm. Algebra 2(1):111–137.
   Web of Science ®Google Scholar
• Xi, C. C. (2021). Frobenius bimodules and flat-dominant dimensions. Sci. China Math. 64(1):33–44. DOI: 10.1007/s11425-018-9519-2.
   Web of Science ®Google Scholar
• Xi, C. C., Yin, S. J. (2020). Cellularity of centrosymmetric martrix algebras and Frobenius extensions. Linear Algebra Appl. 590:317–329. DOI: 10.1016/j.laa.2020.01.002.
   Web of Science ®Google Scholar
• Zhao, Z. B. (2019). Gorenstein homological invariant properties under Frobenius extensions. Sci. China Math. 62(12):2487–2496. DOI: 10.1007/s11425-018-9432-2.
   Web of Science ®Google Scholar