CAJ | 학술논문

设R为一环,ωR为Tor-自正交模.引入模的右Tor-正交维数(相对于ωR)这一概念,并且给出了一种计算模的这种相对右Tor-正交维数的准则.对一个交换、凝聚的半局部环R和一有限表示的Tor-自正交模R-模ω,将证明ω的平坦维数与R/J的右Tor-正交维数(相对于ωR)是相等的,其中J为环R的Jacobson根.作为上述结果的推论,得到了ω有有限的平坦维数当且仅当每一个(有限表示的)R-模有有限的右Tor-正交维数(相对于ωR)的结论.最后,若ωR是—Tor-倾斜模,得到了一个左R-模有有限右Tor-正交维数(相对于ωR)的一些等价条件.
설R위일배,ωR위Tor-자정교모.인입모적우Tor-정교유수(상대우ωR)저일개념,병차급출료일충계산모적저충상대우Tor-정교유수적준칙.대일개교환、응취적반국부배R화일유한표시적Tor-자정교모R-모ω,장증명ω적평탄유수여R/J적우Tor-정교유수(상대우ωR)시상등적,기중J위배R적Jacobson근.작위상술결과적추론,득도료ω유유한적평탄유수당차부당매일개(유한표시적)R-모유유한적우Tor-정교유수(상대우ωR)적결론.최후,약ωR시—Tor-경사모,득도료일개좌R-모유유한우Tor-정교유수(상대우ωR)적일사등개조건.
Let R be a ring and ωR a Tor-self-orthogonal module. The notion of the right Tor-orthogonal dimension (relative to ωR) of modules was introduced and a criterion for computing this relative right Tororthogonal dimension of modules was given.For a commutative coherent and semilocal ring R and a finitely presented Tor-self-orthogonal R-module ω,it was shown that the flat dimension of ω and the right Tor-orthogonal dimension (relative to ω) of R/J are identical,where J is the Jacobson radical of R.As a consequence,it was obtained that ω has a finite flat dimension if and only if every (finitely presented) R-module has a finite right Tor-orthogonal dimension (relative to ω).If ωR is a Tor-tilting module,then some equivalent conditions of a left R-module has a finite right Tor-orthogonal dimension (relative to ωR).