《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (2): 51-57.doi: 10.6040/j.issn.1671-9352.0.2022.054
• • 上一篇
陈文静,李玲
CHEN Wen-jing, LI Ling
摘要： 引入了左(右)n-Frobenius对和特殊的左(右)n-Frobenius对的定义,研究了它们的性质,讨论了左(右)n-Frobenius对和右(左)n-余挠对之间的关系,给出了特殊的左(右)n-Frobenius对的等价刻画。最后给出了特殊的左(右)n-Frobenius对的一些应用,以及左完全的QF环的等价刻画。
中图分类号:
| [1] SALCE L. Cotorsion theories for Abelian groups[J]. Symposia Mathematica, 1979, 23:11-32. [2] HUERTA M, MENDOZA O, PÉREZ M A. n-Cotorsion pairs[J]. Journal of Pure and Applied Algebra, 2021, 225(5):106556. [3] BECERRIL V, MENDOZA O, PÉREZ M A, et al. Frobenius pairs in Abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts[J]. Journal of Homotopy and Related Structures, 2019, 14(1):1-50. [4] CHEN W J, LI L, RAO Y P. Model structures and recollements induced by duality pairs[EB/OL].[2022-08-09]. https://doi.org/10.48550/arXiv.2108.00140 [5] CHEN W J, LIU Z K. Model structures, recollements and duality pairs [J]. Journal of Algebra and Its Applications, 2021: 2350017. [6] CHEN W J, LIU Z K, YANG X Y. A new method to construct model structures from a cotorsion pair[J]. Communications in Algebra, 2019, 47(11):4420-4431. [7] LIANG L, YANG G. Constructions of Frobenius pairs in Abelian categories[J]. Mediterranean Journal of Mathematics, 2022, 19(2):1-17. [8] ENOCHS E E, JENDA O M G. Relative homological algebra[M] //De Gruyter Expositions in Mathematics, Vol 30, Berlin: Walter de Gruyter & Co, 2000. [9] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220(1):611-633. [10] DING N Q, LI Y L, MAO L X. Strongly Gorenstein flat modules[J]. Journal of the Australian Mathematical Society, 2009, 86(3):323-338. [11] BRAVO D, GILLESPIE J, HOVEY M. The stable module category of a general ring[J]. [2022-08-09]. https://doi.org/10.48550/arXiv.1405.5768 [12] GILLESPIE J. Duality pairs and stable module categories[J]. Journal of Pure and Applied Algebra, 2019, 223(8):3425-3435. [13] BECERRIL V, MENDOZA O, SANTIAGO V. Relative Gorenstein objects in Abelian categories[J]. Communications in Algebra, 2021, 49(1):352-402. [14] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189(1/2/3):167-193. |
| [1] | 任叶菲,梁力. Frobenius对的应用[J]. 《山东大学学报(理学版)》, 2022, 57(10): 39-43. |
|
||
