Frobenius扩张下的Gc-投射(内射)复形
Gc-Projective (Injective) Complex under Frobenius Extension
摘要: 本文利用类比归纳的方法，证明了Gc-投射(Gc-内射)复形是投射(内射)可解的，以及在Frobenius 扩张下，复形的Gc-投射性和内射性是保持的。进一步，得到了在Frobenius扩张下，复形的Gc-投射维数和内射维数是不变的。
Abstract: In this paper, by using the method of analogical induction, we prove that Gc-projective (Gc-injective) complexes are projectively (injectively) resolving and the Gc-projective (Gc-injective) properties of the complexes are preserved under the Frobenius exten-sion. Further, we obtain that Gc-Projective (Gc-injective) dimensions of the complexes are invariant under the Frobenius exteiLsion.
文章引用：徐启帆. Frobenius扩张下的Gc-投射(内射)复形[J]. 应用数学进展, 2022, 11(12): 9066-9071. https://doi.org/10.12677/AAM.2022.1112956

参考文献

[1] Holm, H. and Wliite, D. (2007) Foxby Exiuivaleuce ov-er Associative Rings. Kyoto Journal of Mathematics. 47. 781-808.
https://doi.org/10.1215/kjm/1250692289
[2] Wliite, D. (2010) Goreusteiu Projective Dimension with Respect to a Seinidualizing Module. Joumul of Commutative AUjebiu^ 2, 111-137.
https://doi.org/10.1216/JCA-2010-2-l-lll
[3] Yang. C.H. and Li, L. (2012) Gorenstein Injective and Projective Complexes with Respect to a Semidualiziug Module. Communication in Algebra, 40, 3352-3364.
https://doi.org/10.1080/00927872.2011.568030
[4] 杨春花.复形的结构与模的Gorenstdii维数[D]:[博士学位论文].南京：南京大学，2011.
[5] Zhao, Z.B. (2022) -Projectivity and Injectivity under Frobenius Extensions. Communica¬tions in Algebra, 50. 5155-5170.
[6] Huaiig, C.L. (2012) -Projective, Injective and Flat Modules under Change of Rings. Joumul of Algebra and Its Applications, 11. Article ED: 1250032.
https://doi.org/10.1142/S0219498811005567
[7] Holm, H. (2004) GoreiLStein Homological Dimensions. Journal of Pure and Applied Ahjebiu, 189. 167-193.
https：//doi.org/10.1016/j,jpaa.2003.11.007
[8] Auslander, M. and Bridger, M. (1969) Stable Module Theory. In: Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, ProvidenceN Rhode Lslaiid.
https://doi.org/10.1090/rnemo/0094

为你推荐