Commutative ideal theory without finiteness conditions: Completely irreducible ideals-Reference-Cited by-同舟云学术

Commutative ideal theory without finiteness conditions: Completely irreducible ideals

Published:2006-03-01 Issue:7 Volume:358 Page:3113-3131
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Fuchs Laszlo,Heinzer William,Olberding Bruce

Abstract

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an irredundant intersection of completely irreducible ideals, and we study the question of uniqueness of such representations. We characterize those commutative rings in which every ideal is an irredundant intersection of completely irreducible ideals.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2006-358-07/S0002-9947-06-03815-3/S0002-9947-06-03815-3.pdf

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