Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Catenarity in module-finite algebras

Authors: Shiro Goto and Kenji Nishida
Journal: Proc. Amer. Math. Soc. 127 (1999), 3495-3502
MSC (1991): Primary 13E05, 16A18; Secondary 13H10, 16A33
Published electronically: May 13, 1999
MathSciNet review: 1618674
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main theorem says that any module-finite (but not necessarily commutative) algebra $\Lambda$ over a commutative Noetherian universally catenary ring $R$ is catenary. Hence the ring $\Lambda$ is catenary if $R$ is Cohen-Macaulay. When $R$ is local and $\Lambda$ is a Cohen-Macaulay $R$-module, we have that $\Lambda$ is a catenary ring, $\dim\Lambda=\dim\Lambda/Q+\mathrm{ht}_\Lambda Q$ for any $Q\in\operatorname{Spec}\Lambda$, and the equality $n=\mathrm{ht}_\Lambda Q- \mathrm{ht}_\Lambda P$ holds true for any pair $P\subseteq Q$ of prime ideals in $\Lambda$ and for any saturated chain $P=P_0\subset P_1\subset \cdots\subset P_n=Q$ of prime ideals between $P$ and $Q$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13E05, 16A18, 13H10, 16A33

Retrieve articles in all journals with MSC (1991): 13E05, 16A18, 13H10, 16A33

Additional Information

Shiro Goto
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-71, Japan

Kenji Nishida
Affiliation: Department of Mathematics, Faculty of Science, Shinsyu University, Matsumoto, 390-0802 Japan

PII: S 0002-9939(99)04962-X
Received by editor(s): October 27, 1997
Received by editor(s) in revised form: February 24, 1998
Published electronically: May 13, 1999
Additional Notes: The first author was supported by the Grant-in-Aid for Scientific Researches (C)
Communicated by: Ken Goodearl
Article copyright: © Copyright 1999 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia