Finiteness in flat modules and algebras

Cox, Susan; Rush, David E.

doi:10.1016/0021-8693(74)90170-7

Cited by 9 publications

(2 citation statements)

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“…Let E be an R-module and the flat T (R)-module (2). Now by Proposition 4.1 (5) we have a t −1 (CSupp R (E)) = Supp T (R) (F ) and a t(Supp T (R) (F )) = CSupp R (E), because a t is surjective. Hence, a t induces an homeomorphism Supp T (R) (F ) → CSupp R (E) for the constructible topology.…”

Section: The Constructible Support Of a Modulementioning

confidence: 97%

Computing the closure of a support

Picavet¹,

Picavet-L’Hermitte²

2022

Preprint

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When E is an R-module over a commutative unital ring R, the Zariski closure of its support is of the form V(O(E)) where O(E) is a unique radical ideal. We give an explicit form of O(E) and study its behavior under various operations of algebra. Applications are given, in particular for ring extensions of commutative unital rings whose supports are closed. We provide some applications to crucial and critical ideals of ring extensions.

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