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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Noninvertible retracts


Author: Joe Yanik
Journal: Proc. Amer. Math. Soc. 87 (1983), 29-32
MSC: Primary 13F20; Secondary 13D15
DOI: https://doi.org/10.1090/S0002-9939-1983-0677224-1
MathSciNet review: 677224
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Abstract: We demonstrate that if $ P$ is a projective $ R[X]$-module that is not stably extended from an $ R$-module, then the symmetric algebra of $ P$ over $ R[X]$ is a retract of a polynomial ring over $ R$, but is not an invertible $ R$-algebra. Hence, there are noninvertible retracts over a quite general class of rings.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0677224-1
Keywords: Retract, invertible algebra, symmetric algebra, module of differentials
Article copyright: © Copyright 1983 American Mathematical Society