《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 1-6.doi: 10.6040/j.issn.1671-9352.0.2022.227
• • 下一篇
张晓磊1,齐薇1,夏伟恒2
ZHANG Xiao-lei1, QI Wei1, XIA Wei-heng2
摘要： 通过局部化角度刻画了τq-PF环。其次,引入并研究了τq-P-平坦模并证明环R是τq-PF环当且仅当任意(主)理想是τq-P-平坦模。最后,从环的有限直积和合并代数角度研究了τq-PF环。此外,给出一些例子区分τq-PF环和PF环。
中图分类号:
| [1] GLAZ S. Commutative coherent rings[M] // Lecture Notes in Mathematics, Vol 1371, Berlin: Spring-Verlag, 1989. [2] GLAZ S. Controlling the zero divisors of a commutative ring[M] // Commutative Ring Theory and Applications(Fez, 2001), Volume 231 of Lecture Notes in Pure and Appl Math. New York: Marcel Dekker Inc, 2003: 191-212. [3] CHENIOUR F, MAHDOU N. When every principal ideal is flat[J].Portugaliae Math, 2011, 70:51-58. [4] WANG Fanggui, MCCASLAND R L. On w-modules over strong moridomains[J]. Commun Algebra,1997, 25(4):1285-1306. [5] YIN Huayu, WANG Fanggui, ZHU Xiaosheng, et al. w-modules over commutative rings[J].J Korean Math Soc, 2011, 48(1):207-222. [6] WANG Fanggui, KIM H. w-injective modules and w-semi-hereditary rings[J]. J Korean Math Soc, 2014, 51:509-525. [7] WANG Fanggui, QIAO Lei. The w-weak global dimension of commutative rings[J]. Bull Korean Math Soc, 2015, 52(4):1327-1338. [8] 夏伟恒,乔磊,宋菲菲.交换环上的w-P-平坦模及其应用[J].吉林大学学报(理学版), 2022, 60(2):269-276. XIA Weiheng, QIAO Lei, SONG Feifei. w-P-flat modules over commutative rings and their applications[J]. Journal of Jilin University(Science Edition), 2022, 60(2):269-276. [9] WANG Fanggui, ZHOU Dechuan, CHEN Dan. Module-theoretic characterizations of the ring of finite fractions of acommutative ring[J]. J Commut Algebra, 2022, 14(1):141-154. [10] WANG Fanggui, ZHOU Dechuan, KIM H, et al. Every Prüfer ring does not have small finitistic dimension at most one[J].Comm Algebra, 2020, 48(12):5311-5320. [11] CAHEN P J, FONTANA M, FRISCH S, et al. Open problems in commutative ring theory[M] //FONTANA M, FRISCH S, GLAZ S, eds. Commutative Algebra. New York: Springer, 2014. [12] ZHOU Dechuan, KIM H, WANG Fanggui, et al. A new semistar operation on a commutative ring and its applications[J]. Comm Algebra, 2020, 48(9):3973-3988. [13] ZHANG Xiaolei. On τq-flatness and τq-coherence[J/OL]. https://arxiv.org/abs/2111.03417. [14] ZHANG Xiaolei, WANG Fanggui. The small finitistic dimensions over commutative rings[J/OL]. J Commut Algebra, https://arxiv.org/abs/2103.08807. [15] HATTORI A. A foundation of torsion theory for modules over general rings[J]. Nagoya Math J, 1960, 17:147-158. [16] WANG Fanggui, KIM H. Foundations of commutative rings and their modules[M]. Singapore: Springer, 2016. [17] FUCHS L, SALCE L. Modules over non-Noetherian domains[M]. Providence: AMS, 2001. [18] ZHANG Xiaolei. A homological characterization of Q0-Prüfer v-multiplication rings[J]. Int Electron J Algebra, 2022, 32:228-240. [19] 李珊珊. P-平坦模,P-内射模和某些环[D]. 成都:四川师范大学, 2005. LI Shanshan. P-fat modules, P-injective modules and some rings[D]. Chengdu: Sichuan Normal University, 2005. [20] COUCHOT F. Flat modules over valuation rings[J]. J Pure Appl Algebra, 2007, 211(1):235-247. [21] D'ANNA M. A construction of Gorenstein rings[J]. J Algebra, 2006, 306:507-519. [22] D'ANNA M, FONTANA M. An amalgamated duplication of a ring along a multiplicative-canonicali deal[J]. Arkiv Mat, 2007, 6:241-252. |
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