Continuous homomorphisms and rings of injective dimension one
نویسندگان
چکیده
منابع مشابه
On semiperfect rings of injective dimension one
We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.
متن کاملTorsionfree Dimension of Modules and Self-injective Dimension of Rings
Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...
متن کاملLocal Cohomology and Gorenstein Injective Dimension over Local Homomorphisms
Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstei...
متن کاملGorenstein injective dimension, Bass formula and Gorenstein rings
Let (R,m, k) be a noetherian local ring. It is well-known that R is regular if and only if the injective dimension of k is finite. In this paper it is shown that R is Gorenstein if and only if the Gorenstein injective dimension of k is finite. On the other hand a generalized version of the so-called Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension. ...
متن کاملWeak dimension of FP-injective modules over chain rings
It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2. This implies that the projective dimension of any countably generated FP-injective module over an Archimedean chain ring is less or equal to 3. By [7, Theorem 1], for any module G over a commutative arithmetical ring R the weak dimension of G ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2012
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-15203