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 large condition for rings with Krull dimension

Author: Ann K. Boyle
Journal: Proc. Amer. Math. Soc. 72 (1978), 27-32
MSC: Primary 16A55
MathSciNet review: 503524
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A module M with Krull dimension is said to satisfy the large condition if for any essential submodule L of M, the Krull dimension of $ M/L$ is strictly less than the Krull dimension of M. For a right noetherian ring R with Krull dimension $ \alpha $ this is equivalent to the condition that every f.g. uniform submodule of $ E({R_R})$ with Krull dimension $ \alpha $ is critical. It is also shown that if R is right noetherian with Krull dimension $ \alpha $ and if $ {I_0}$ is a right ideal maximal with respect to K $ \dim {I_0} < \alpha $, then R satisfies the large condition if and only if $ {I_0}$ is a finite intersection of cocritical right ideals and $ {I_0}$ is closed.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A55

Retrieve articles in all journals with MSC: 16A55

Additional Information

Keywords: The large condition, semicritical module, semiprime ring, nonsingularly k-primitive ring
Article copyright: © Copyright 1978 American Mathematical Society