JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (2): 105-109.doi: 10.6040/j.issn.1671-9352.0.2022.512

Previous Articles     Next Articles

Stability function and torsion theory on exact categories

Zheng XIN(),Dingguo WANG,Tiwei ZHAO*()   

  1. School of Mathematical Sciences, Jining Normal University, Qufu 273165, Shandong, China
  • Received:2022-09-29 Online:2024-02-20 Published:2024-02-20
  • Contact: Tiwei ZHAO E-mail:xinzheng1314@yeah.net;tiweizhao@qfnu.edu.cn

RichHTML

0

PDF (PC)

78

Abstract:

Stability function on exact categories is studied, and torsion classes and torsion-free classes are constructed by using the stability functions. Then, a class of torsion pairs is obtained.

Key words: exact category, stability function, torsion pair

CLC Number: 

  • O154.2
1 MUMFORD D . Geometric invariant theory[M]. New York: Academic Press, 1965.
2 SCHOFIELD A . Semi-invariants of quivers[J]. Journal of the London Mathematical Society, 1991, 43 (3): 385- 395.
3 KING A D . Moduli of representations of finite dimensional algebras[J]. The Quarterly Journal of Mathematics, 1994, 45 (4): 515- 530.
doi: 10.1093/qmath/45.4.515
4 RUDAKOV A . Stability for an Abelian category[J]. Journal of Algebra, 1997, 197, 231- 245.
doi: 10.1006/jabr.1997.7093
5 BRUSTLE T , SMITH D , TREFFINGER H . Stability conditions and maximal Green sequences in Abelian categories[J]. Revista de la Union Matematica Argentina, 2022, 63 (1): 203- 221.
6 DICKSON S E . A torsion theory for Abelian categories[J]. Transactions of the American Mathematical Society, 1966, 121, 223- 235.
doi: 10.1090/S0002-9947-1966-0191935-0
7 BRIDGELAND T . Scattering diagrams, hall algebras and stability conditions[J]. Algebraic Geometry, 2017, 4 (5): 523- 561.
8 QUILLEN D. Higher algebraic K-theory: I[C]// Algebraic K-theory. Berlin: Springer, 1973, 341: 85-147.
9 BUHLER T . Exact categories[J]. Expositiones Mathematicae, 2010, 28 (1): 1- 69.
doi: 10.1016/j.exmath.2009.04.004
10 ENOMOTO H . Schur̓s lemma for exact categories implies Abelian[J]. Journal of Algebra, 2021, 584, 260- 269.
doi: 10.1016/j.jalgebra.2021.05.017
11 HASSOUN S, ROY S. Admissible intersection and sum property [EB/OL]. (2020-06-05)[2022-09-29]. http://arxiv.org/abs/1906.03246v3.
[1] CHEN Wen-jing, LI Ling. n-Frobenius pairs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(2): 51-57.
[2] YUAN Qian-qian, YAO Hai-lou. On silting comodules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 1-7.
[3] ZHAO Jun-xiu, DI Rong-rong, DI Zhen-xing. n-IFP-gr-injective modules and n-IFP-gr-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 99-103.
[4] ZHANG Ping-er, YANG Xiao-yan. A new construction method of triangulated model structures [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 97-102.
[5] WANG Zhan-ping, YUAN Kai-ying. Strongly Gorenstein injective modules with respect to a cotorsion pair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 102-107.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] CHENG Zhi1,2, SUN Cui-fang2, WANG Ning1, DU Xian-neng1. On the fibre product of Zn and its property[J]. J4, 2013, 48(2): 15 -19 .
[2] ZHANG Ai-ping,LI Gang . LRquasinormalEhresmann semigroups[J]. J4, 2006, 41(5): 44 -47 .
[3] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
[4] MA Jian-ling . Spectral characterization of the rhomb-type achromatic retarder[J]. J4, 2007, 42(7): 27 -29 .
[5] HUO Yu-hong, JI Quan-bao. Synchronization analysis of oscillatory activities in a biological cell system[J]. J4, 2010, 45(6): 105 -110 .
[6] SHI Chang-guang . Multi-soliton solution of the Faddeev model[J]. J4, 2007, 42(7): 38 -40 .
[7] MA Jie-xiong,JIANG Li,QI Yu-yu,XIANG FEng-ning,XIA Guang-min . The growth of calli and regenerated plantlets of Gentiana Przewalskii Maxim. and the constituents analysis of its two effective components[J]. J4, 2006, 41(6): 157 -160 .
[8] BIAN Pei,HE Hai-lun,CHEN Xiu-lan,ZHANG Yu-zhong . [J]. J4, 2006, 41(5): 166 -172 .
[9] WANG Zhen and ZHANG Jin . A conservative numerical scheme and its convergence analysis for a class of the NLS equation[J]. J4, 2007, 42(3): 13 -17 .
[10] WANG Kang, LI Hua. Analysis of the compound Haqing injection with hyphenated chromatography and chemometric resolution[J]. J4, 2009, 44(11): 16 -20 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd