Anti-isomorphisms and the failure of duality

A. L.S. Corner; B. Goldsmith; S. L. Wallutis

doi:10.1515/9783110203035.315

Anti-isomorphisms and the failure of duality

A. L.S. Corner, B. Goldsmith, S. L. Wallutis

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Groups and modules with isomorphic endomorphism rings are known, in certain cases, to be necessarily isomorphic. When such a ring isomorphism is replaced by an anti-isomorphism, the modules are often determined only up to isomorphism of certain duals. This type of situation is examined in a number of cases with special emphasis on the situation for mixed Abelian groups, where it is shown that no reasonable duality may exist.

Original language	English
Title of host publication	Models, Modules and Abelian Groups
Subtitle of host publication	In Memory of A. L. S. Corner
Publisher	Walter de Gruyter GmbH and Co. KG
Pages	315-323
Number of pages	9
ISBN (Print)	9783110194371
DOIs	https://doi.org/10.1515/9783110203035.315
Publication status	Published - 10 Dec 2008
Externally published	Yes

Keywords

Anti-isomorphism
Baer-kaplansky theorem
Mixed abelian groups

Access to Document

10.1515/9783110203035.315

https://arrow.tudublin.ie/scschmatbk/2Licence: CC BY-NC-SA

Cite this

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AU - Corner, A. L.S.

AU - Goldsmith, B.

AU - Wallutis, S. L.

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N2 - Groups and modules with isomorphic endomorphism rings are known, in certain cases, to be necessarily isomorphic. When such a ring isomorphism is replaced by an anti-isomorphism, the modules are often determined only up to isomorphism of certain duals. This type of situation is examined in a number of cases with special emphasis on the situation for mixed Abelian groups, where it is shown that no reasonable duality may exist.

AB - Groups and modules with isomorphic endomorphism rings are known, in certain cases, to be necessarily isomorphic. When such a ring isomorphism is replaced by an anti-isomorphism, the modules are often determined only up to isomorphism of certain duals. This type of situation is examined in a number of cases with special emphasis on the situation for mixed Abelian groups, where it is shown that no reasonable duality may exist.

KW - Anti-isomorphism

KW - Baer-kaplansky theorem

KW - Mixed abelian groups

UR - https://www.scopus.com/pages/publications/84882014100

U2 - 10.1515/9783110203035.315

DO - 10.1515/9783110203035.315

M3 - Chapter

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SP - 315

EP - 323

BT - Models, Modules and Abelian Groups

PB - Walter de Gruyter GmbH and Co. KG

ER -

Anti-isomorphisms and the failure of duality

Abstract

Keywords

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