Abstract
Let N be a completely prime ideal of a right distributive ring A, and let \( N \subseteq J(A). \) Then the following assertions hold.
-
(1)
N = mN ⊂ mA for all m ∈ A\N, and A has no nontrivial idempotents.
-
(2)
N is comparable to any right ideal of A.
-
(3)
M N = N for any right ideal M of A which is not contained in N.
-
(4)
Either N = 0 and A is a right uniform domain, or N is a nonzero essential right ideal of A.
-
(5)
Either the module NA IS not uniform, or A is right uniform.
-
(6)
If N is a finitely generated left ideal, then either N = J(A), or N = 0 and A is a right uniform domain.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Tuganbaev, A.A. (1998). Distributive rings with maximum conditions. In: Semidistributive Modules and Rings. Mathematics and Its Applications, vol 449. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5086-6_9
Download citation
DOI: https://doi.org/10.1007/978-94-011-5086-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6136-0
Online ISBN: 978-94-011-5086-6
eBook Packages: Springer Book Archive