Non-self-injective injective hulls with compatible multiplication

Victor Camillo; Ivo Herzog; Pace P Nielsen

doi:10.1016/j.jalgebra.2007.03.016

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Non-self-injective injective hulls with compatible multiplication

Journal article

Open access

Peer reviewed

Non-self-injective injective hulls with compatible multiplication

Victor Camillo, Ivo Herzog and Pace P Nielsen

Journal of algebra, Vol.314(1), pp.471-478

2007

DOI: 10.1016/j.jalgebra.2007.03.016

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Abstract

Let R be a ring, and let S be the injective hull of the right regular module R R . Suppose that S can be made into a ring with multiplication compatible with that of R. Osofsky, in 1964, asked if S S is necessarily injective. We construct examples giving a negative answer to this question, and even construct an infinite chain of such rings.

Maximal quotient ring

Injective hull

Compatible multiplication

Essential extension

Details

Title: Subtitle: Non-self-injective injective hulls with compatible multiplication
Creators: Victor Camillo - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Ivo Herzog - Department of Mathematics, The Ohio State University at Lima, Lima, OH 45804, USA
Pace P Nielsen - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: Journal of algebra, Vol.314(1), pp.471-478
DOI: 10.1016/j.jalgebra.2007.03.016
ISSN: 0021-8693
eISSN: 1090-266X
Publisher: Elsevier Inc
Language: English
Date published: 2007
Academic Unit: Mathematics
Record Identifier: 9983985852702771

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