the behavior of homological dimensions
نویسندگان
چکیده
let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.
منابع مشابه
The behavior of homological dimensions
Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.
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Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.
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متن کاملhomological dimensions of complexes of r-modules
let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.
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In 1969 Kunz [Ku] proved a fundamental result, connecting the regularity of a local ring of positive characteristic with the flatness of its Frobenius endomorphism φ. This was a first indication of the important role that φ would play in homological commutative algebra, especially in reflecting basic homological properties of the ring. Some results in Peskine and Szpiro’s groundbreaking thesis,...
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عنوان ژورنال:
نظریه تقریب و کاربرد های آنجلد ۷، شماره ۱، صفحات ۱-۱۰
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