PGF-模和强半Gorenstein-投射模  

PGF-modules and strongly semi-Gorenstein-projective modules

作　　者：白九红 梁力[1] BAI Jiu-hong;LIANG Li(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2021年第8期105-110,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761045);兰州交通大学“百名青年优秀人才培养计划”资助项目。

摘　　要：令SSGP表示所有强半Gorenstein-投射模构成的类。给出了PGF-模与强半Gorenstein-投射模的关系,证明了在任意环R上,SSGP∩P GF=PGF,进而得到SSGP=PGF当且仅当SSGP⊆P GF,其中PGF是所有PGF-模构成的类,P GF是所有PGF-维数有限的模构成的类。最后证明了环R的有限型PGF-维数和有限型投射维数相等。Let SSGP denote the class of all strongly semi-Gorenstein-projective modules.Some relations between PGF-modules and strongly semi-Gorenstein-projective modules are given,and over an arbitrary ring R,SSGP∩P GF=PGF is proved.It is got that SSGP=PGF if and only if SSGP⊆P GF,where PGF is the class of all PGF-modules,and P GF is the class of all R-modules with finite PGF-dimension.Finally,the finitistic PGF-dimension of a ring R is equal to the finitistic projective dimension is proved.

关 键 词：PGF-模 强半Gorenstein-投射模 有限型PGF-维数 有限型投射维数 

分 类 号：O154.2[理学—数学]