Injective modules under flat base change

Hans‐Bjørn Foxby

Type: Article

Publication Date: 1975-01-01

Citations: 14

DOI: https://doi.org/10.1090/s0002-9939-1975-0409439-7

Abstract

It is proved that an injective module after a flat change of base is of pointwise finite injective dimension if and only if all the fibers at points associated to the injective module are Gorenstein rings (or trivial).

Locations

Proceedings of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Injective Modules Under Flat Base Change	1975	Hans‐Bjørn Foxby
+	Gorenstein Injective and Gorenstein Flat Dimensions Under Base Change	2003	Leila Khatami Siamak Yassemi
+ PDF Chat	Injective modules under change of rings	1965	Ernst Snapper
+ PDF Chat	Injective Modules Under Change of Rings	1965	Ernst Snapper
+	Gorenstein Dimensions under Base Change	2002	Leila Khatami Siamak Yassemi
+	Flat modules, injective modules and quotient rings	1971	Kiiti Morita
+ PDF Chat	Minimal Injective Resolutions Under Flat Base Change	1977	Hans‐Bjørn Foxby Anders Thorup
+	Ω-Gorenstein Projective, Injective and Flat Modules	2011	Yang Xiaoyan Zhongkui Liu
+ PDF Chat	Structure of flat covers of injective modules	2003	Sh. Payrovi M. Akhavizadegan
+	A Generalization of Gorenstein Injective and Flat Modules	2016	Lu Bo
+ PDF Chat	GORENSTEIN PROJECTIVE, INJECTIVE AND FLAT MODULES	2009	Zhongkui Liu Yang Xiaoyan
+	Injective endomorphism modules	2009	Theodore G. Faticoni
+ PDF Chat	Flat Covers of Modules	1996	Jinzhong Xu
+ PDF Chat	C-Gorenstein projective, injective and flat modules	2010	Xiao Yan Yang Zhong Kui Liu
+	The flat dimensions of injective modules	1993	Nanqing Ding Jianlong Chen
+	Injective hulls of flat modules	1980	T. Cheatham Edgar E. Enochs
+ PDF Chat	Gorenstein dimensions in trivial ring extensions	2009	Najib Mahdou Khalid Ouarghi
+	Report on injective modules	1965	Cheng-Chiang Tsai
+	A Note on Duality of Flat Module and Injective Modules	2007	Fan Zheng-en
+	INJECTIVE CONVERS UNDER CHANGE OF RINGS	2001	Yeong Moo Song Hae Sik Kim

Works That Cite This (14)

Action	Title	Year	Authors
+ PDF Chat	Adic semidualizing complexes	2020	Sean Sather-Wagstaff Richard Wicklein
+	Complete intersection dimensions and Foxby classes	2008	Sean Sather-Wagstaff
+ PDF Chat	Minimal injective resolutions under flat base change	1977	Hans‐Bjørn Foxby Anders Thorup
+	ON POINCARÉ SERIES	1978	S S Strogalov
+	Modules	1983	V. T. Markov A. V. Mikhalëv L. A. Skornyakov A. A. Tuganbaev
+ PDF Chat	Complete Intersection Hom Injective Dimension	2020	Sean Sather-Wagstaff Jonathan Totushek
+ PDF Chat	Minimal Injective Resolutions Under Flat Base Change	1977	Hans‐Bjørn Foxby Anders Thorup
+ PDF Chat	The Category of Graded Modules.	1974	Robert M. Fossum Hans-Bj�rn Foxby
+	The Frobenius functor and injective modules	2014	Thomas Marley
+	<i>G<sub>C</sub></i>-PROJECTIVE, INJECTIVE AND FLAT MODULES UNDER CHANGE OF RINGS	2011	Chaoling Huang

Works Cited by This (2)

Action	Title	Year	Authors
+	On the ubiquity of Gorenstein rings	1963	Hyman Bass
+	Class groups of n-noetherian rings	1968	Luther Claborn Robert M. Fossum