Cancellation ideals of a ring extension

Document Type

Article

Publication Date

1-1-2021

Publication Title

Algebra and Discrete Mathematics

Abstract

We study properties of cancellation ideals of ring extensions. LetR ⊆ S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R ⊆ S if whenever IB = IC for two S-regular (finitely generated) R-submodules B and C of S, then B = C. We show that a finitely generated ideal I is a cancellation ideal of the ring extension R ⊆ S if and only if I is S-invertible.

Department

Mathematics

Volume Number

32

Issue Number

1

First Page

138

Last Page

146

DOI

10.12958/adm1424

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