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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
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 ``$ 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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DOI: https://doi.org/10.1090/S0002-9939-1974-0330130-9
Keywords: Polynomial ring, projective module, projective ideal, content, finitely generated ideal, idempotent element
Article copyright: © Copyright 1974 American Mathematical Society