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Inventiones mathematicae

, Volume 209, Issue 2, pp 463–479 | Cite as

On the non-existence of right almost split maps

  • Jan Šaroch
Article

Abstract

We show that, over any ring, a module C is the codomain of a right almost split map, if and only if C is finitely presented with a local endomorphism ring. Thus we answer a 40-year-old question by Maurice Auslander.

Mathematics Subject Classification

Primary 16G70 Secondary 16D10 16E30 

Notes

Acknowledgements

I would like to express my gratitude to Dolors Herbera for inviting me to participate on the project MTM2011-28992-C02-01 of DGI MINECO (Spain). Significant part of the material in this paper was written during my stay at Universitat Autònoma de Barcelona from 20  March to 1 April 2015. Many thanks also to Jan Trlifaj and Ivo Herzog for reading and discussing the vast majority of the text, and to the anonymous referees for their suggestions which helped to improve the quality of the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Algebra, Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

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