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)



The Laskerian property, power series rings and Noetherian spectra

Authors: Robert Gilmer and William Heinzer
Journal: Proc. Amer. Math. Soc. 79 (1980), 13-16
MSC: Primary 13E05; Secondary 13J05
MathSciNet review: 560575
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if the power series ring $ R[[X]]$ in one indeterminate over a commutative ring R with identity is Laskerian, then R is Noetherian. On the other hand, if $ R[[X]]$ is a ZD-ring, then R has Noetherian spectrum, but R need not be Noetherian. We show that, in general, a Laskerian ring has Noetherian spectrum.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13E05, 13J05

Retrieve articles in all journals with MSC: 13E05, 13J05

Additional Information

Keywords: Laskerian ring, power series ring, Noetherian, ZD-ring, Noetherian spectrum
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society