Frobenius扩张下模的无挠性和自反性

doi:10.6040/j.issn.1671-9352.0.2021.623

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 52-58.doi: 10.6040/j.issn.1671-9352.0.2021.623

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Frobenius扩张下模的无挠性和自反性

周芮,赵志兵^*

安徽大学数学科学学院, 安徽合肥 230601

发布日期:2022-10-06
作者简介:周芮(1997— ),女,硕士研究生,研究方向为环与代数表示论. E-mail:2443537372@qq.com *通信作者简介:赵志兵(1979— ),男,博士,讲师,研究方向为环与代数表示论. E-mail:zbzhao@ahu.edu.cn
基金资助:
国家自然科学基金资助项目(11871071);安徽省高校自然科学研究重点项目(KJ2019A0007)

Torsionfreeness and reflexivity under Frobenius extensions

ZHOU Rui, ZHAO Zhi-bing^*

School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China

Published:2022-10-06

摘要/Abstract

摘要： 设A/R是环的Frobenius扩张。证明了在环的Frobenius扩张下,一个模的无挠性和自反性是保持的,即对于任意的A-模 M,M_A是无挠模(或自反模)当且仅当M作为R-模是无挠模(或自反模)。

关键词: 无挠模, 自反模, Frobenius扩张

Abstract: Let A/R be a Frobenius extension of rings, we prove that torsionfreeness and reflexivity of modules are preserved under Frobenius extension, that is, for an A-module M, M_A is torsionfree(resp. reflexive)as an A-module if and only if M is torsionfree(resp. reexive)as an R-module.

Key words: torsionfree modules, reflexive modules, Forbenius extensions

中图分类号:

O154.2

周芮,赵志兵. Frobenius扩张下模的无挠性和自反性[J]. 《山东大学学报(理学版)》, 2022, 57(10): 52-58.

ZHOU Rui, ZHAO Zhi-bing. Torsionfreeness and reflexivity under Frobenius extensions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 52-58.

参考文献

[1] KASCH F. Grundlagen einer theorie der Frobenius-Erweiterungen[J]. Math Ann, 1954, 127:453-474.
[2] NAKAMAYA T, TSUZUKU T. On Frobenius extension Ⅰ[J]. Nagoya Math J, 1960, 17:89-110.
[3] NAKAMAYA T, TSUZUKU T. On Frobenius extension Ⅱ[J]. Nagoya Math J, 1961, 19:127-148.
[4] MORITA K. Adojint pairs of functors and Frobenius extension[J]. Sci Rep ToykoKyoikuDaigaku(Sect. A), 1965, 9:40-71.
[5] XI Changchang. Frobenius bimodules and flat-dominant dimensions[J]. Sci China Math, 2021, 64:33-44.
[6] KADISON L. New examples of Frobenius extensions[M] //University Lecture Series 14. Provedence: Amer Math Soc, 1999.
[7] AUSLANDER M, BRIDGER M. Stable module theory[M]. New York: Memoirs of the American Mathematical Society, 1969: 94.
[8] ANDERSON F W, FULLER K R. Rings and categories of modules[M]. New York: Springer-Verlag, 1974.
[9] HUANG Zhaoyong. Selforthogonal modules with finite injective dimension III[J]. Algebra Rep Theory, 2009, 12:371-384.
[10] AUSLANDER M. Coherent functors[M]. Berlin: Springer, 1966.
[11] HUANG Zhaoyong. ω-k-torsionfree modules and ω-left approximation dimension[J]. Science in China Series A Mathematics, 2001, 44(2):184-192.
[12] AUSLANDER M, REITEN I. Applications of contravariantly fnite subcategories[J]. Advances in Mathematics, 1991, 86(1):111-152.
[13] ZHAO Zhaobing. Gorenstein homological invariant properties under Frobenius extensions[J]. Sci China Math, 2019, 62:2487-2496.
[14] REN Wei. Gorenstein projective and injective dimensions over Frobenius extensions[J]. Comm Algebra, 2018, 46:1-7.
[15] 徐辉, 赵志兵. 相对无挠模[J]. 山东大学学报(理学版), 2017, 52:75-80. XU Hui, ZHAO Zhibing. Relatively torsionfree modules[J]. Journal of Shandong University(Natural Science), 2017, 52:75-80.

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Frobenius扩张下模的无挠性和自反性

Torsionfreeness and reflexivity under Frobenius extensions

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