关于半对偶模的两个特殊模类及投射维数  

Two Special Classes of Modules and Projective Dimensions with Respect to a Semidualizing Module

作　　者：何东林[1] HE Donglin(School of Mathematics and Information Sciences,Longnan Teachers College,Longnan 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院,甘肃陇南742500

出　　处：《湖北民族大学学报（自然科学版）》2020年第2期206-208,共3页Journal of Hubei Minzu University:Natural Science Edition

基　　金：甘肃省高等学校科研项目(2018A-269);甘肃省高等学校创新能力提升项目(2019B-224).

摘　　要：利用同调代数的方法,讨论关于半对偶模W的余自反模类Cor W(R)和伴随余自反模类Acor W(R)的若干性质,其中Cor W(R)表示所有自然同态v N:W R Hom R(W,N)→N为同构的模N组成的类,Acor W(R)表示所有自然同态u M:M→Hom R(W,W R M)为同构的模M组成的类.研究模U的Cor W(R)-覆盖与模Hom R(W,U)的Acor W(R)-覆盖之间的关系,以及模U的Acor W(R)-包络与模W R U的Cor W(R)-包络之间的关系.进而证明了在特定条件下,Hom R(W,U)的Acor W(R)-投射维数小于等于U的Cor W(R)-投射维数,并且W R U的Cor W(R)-投射维数小于等于U的Acor W(R)-投射维数.Using methods of homological algebra,the paper discusses some properties of coreflexive class Cor W(R)and adjoint coreflexive class Acor W(R)with respect to a semidualizing module W,where Cor W(R)denotes the class of all modules N with natural homomorphism v N:W R Hom R(W,N)→N isomorphism,Acor W(R)denotes the class of all modules M with natural homomorphism u M:M→Hom R(W,W R M)isomorphism.The relationships between Cor W(R)-cover of module U and Acor W(R)-cover of module Hom R(W,U),Acor W(R)-envelope of module U and Cor W(R)-envelope of module W R U are investigated.Furthermore,it is proved that Acor W(R)-projective dimension of Hom R(W,U)is less than or equal to Cor W(R)-projective dimension of U,and Cor W(R)-projective dimension of W R U is less than or equal to Acor W(R)-projective dimension of U under certain conditions.

关 键 词：半对偶模 余自反模 伴随余自反模 投射维数 

分 类 号：O153[理学—数学]