τ_(q)-PF环  

τ_(q)-PF Rings

作　　者：张晓磊 齐薇 夏伟恒 ZHANG Xiao-lei;QI Wei;XIA Wei-heng(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255000,Shandong,China;School of Math-ematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255000 [2]四川师范大学数学科学学院,四川成都610066

出　　处：《山东大学学报（理学版）》2023年第3期1-6,13,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12061001);国家自然科学青年基金资助项目(12201361)。

摘　　要：通过局部化角度刻画了τ_(q)-PF环。其次,引入并研究了τ_(q)-P-平坦模并证明环R是τ_(q)-PF环当且仅当任意(主)理想是τ_(q)-P-平坦模。最后,从环的有限直积和合并代数角度研究了τ_(q)-PF环。此外,给出一些例子区分τ_(q)-PF环和PF环。The notion of τ_(q)-P-flat modules is introduced and studied. Specially, a ring R is τ_(q)-PF if and only if any(principal) ideal of R is τ_(q)-P-flat. Finally, τ_(q)-PF rings are also studied in terms of finite direct products of rings and amalgamation algebras. By the way, some examples are given to distinguish τ_(q)-PF rings and PF rings.

关 键 词：τ_(q)-PF环 τ_(q)-P-平坦模 PF环 合并代数 

分 类 号：O154.2[理学—数学]