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Proceedings of the American Mathematical Society

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

 
 

 

Ideals $I$ of $R[X]$ for which $R[X]/I$ is $R$-projective


Authors: J. W. Brewer and W. J. Heinzer
Journal: Proc. Amer. Math. Soc. 43 (1974), 21-25
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0330130-9
MathSciNet review: 0330130
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Abstract: A characterization is given of those ideals $I$ of the polynomial ring $R[X]$ such that $R[X]/I$ is $R$-projective. It is also shown that a commutative ring $R$ has the property β€œ$R[X]/IR$-projective implies $I$ is a finitely generated ideal” if and only if $R$ has only a finite number of idempotents.


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Keywords: Polynomial ring, projective module, projective ideal, content, finitely generated ideal, idempotent element
Article copyright: © Copyright 1974 American Mathematical Society