Injective modules under faithfully flat ring extensions

Lars Winther Christensen; Fatih Köksal

doi:10.1090/proc/12791

Injective modules under faithfully flat ring extensions

Proceedings of the American Mathematical Society ◽

10.1090/proc/12791 ◽

2015 ◽

Vol 144 (3) ◽

pp. 1015-1020 ◽

Cited By ~ 3

Author(s):

Lars Winther Christensen ◽

Fatih Köksal

Keyword(s):

Injective Modules ◽

Flat Ring ◽

Ring Extensions

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Ring Constructions and Generation of the Unbounded Derived Module Category

Algebras and Representation Theory ◽

10.1007/s10468-021-10094-2 ◽

2021 ◽

Author(s):

Charley Cummings

Keyword(s):

Sufficient Conditions ◽

Derived Category ◽

Module Category ◽

Injective Modules ◽

Ring Extensions

AbstractWe consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we say that injectives generate for the ring. In particular, we ask whether, if injectives generate for a collection of rings, do injectives generate for related ring constructions, and vice versa. We provide sufficient conditions for this statement to hold for various constructions including recollements, ring extensions and module category equivalences.

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Cousin complexes and flat ring extensions

Communications in Algebra ◽

10.1080/00927879708825856 ◽

1997 ◽

Vol 25 (1) ◽

pp. 311-339 ◽

Cited By ~ 3

Author(s):

Henrike Petzl

Keyword(s):

Flat Ring ◽

Ring Extensions ◽

Cousin Complexes

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Distortion of steel flat ring products during the production cycle∗

HTM Journal of Heat Treatment and Materials ◽

10.3139/105.110183 ◽

2013 ◽

Vol 68 (2) ◽

pp. 97-102

Author(s):

D. Česnik ◽

V. Bratuš ◽

M. Bizjak

Keyword(s):

Production Cycle ◽

Flat Ring

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Flat Ring Flexure Test for Full-Culm Bamboo

Non-Conventional Materials and Technologies ◽

10.21741/9781945291838-32 ◽

2018 ◽

Cited By ~ 2

Keyword(s):

Flat Ring ◽

Flexure Test

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Extensions of Rings Having McCoy Condition

Canadian Mathematical Bulletin ◽

10.4153/cmb-2009-029-5 ◽

2009 ◽

Vol 52 (2) ◽

pp. 267-272 ◽

Cited By ~ 5

Author(s):

Muhammet Tamer Koşan

Keyword(s):

Positive Integer ◽

Associative Ring ◽

Nonzero Element ◽

Ring Extensions

AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(xn) is a right McCoy ring for any positive integer n ≥ 2.

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