Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

A note on finitely generated ideals which are locally principal


Authors: James W. Brewer and Edgar A. Rutter
Journal: Proc. Amer. Math. Soc. 31 (1972), 429-432
DOI: https://doi.org/10.1090/S0002-9939-1972-0289480-5
MathSciNet review: 0289480
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: Let $ R$ be a commutative ring with identity $ 1 \ne 0$ and let $ A$ be a nonzero ideal of $ R$. A problem of current interest is to relate the notions of ``projective ideal", ``flat ideal'' and ``multiplication ideal". In this note we prove two results which show that the maximal ideals containing the annihilator of $ A$ can play an important role in determining the relationship between these concepts. As a consequence we are able to prove that a finitely generated multiplication ideal in a semi-quasi-local ring is principal, that a finitely generated flat ideal having only a finite number of minimal prime divisors is projective and that for Noetherian rings or semihereditary rings, finitely generated multiplication ideals with zero annihilator are invertible.


References [Enhancements On Off] (What's this?)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289480-5
Keywords: Flat ideal, projective ideal, multiplication ideal, principal ideal
Article copyright: © Copyright 1972 American Mathematical Society