JOURNAL ARTICLE
Maximal Ideals in Rings
Henry E. HeatherlyRalph P. Tucci
Year: 2005 Journal: Quaestiones Mathematicae Vol: 28 (2)Pages: 137-143 Publisher: Taylor & Francis
Abstract
This paper gives necessary and sufficient conditions which guarantee that a ring have maximal left, right, or two-sided ideals. The relations of rings without maximal ideals to the Jacobson and Brown-McCoy radical are discussed. Examples of rings without maximal ideals are given to illustrate the theory. Connections of existence of maximal ideals and the Axiom of Choice in Zermelo-Fraenkel set theory are noted.
Keywords:
Mathematics Maximal ideal Jacobson radical Axiom Ring (chemistry) Pure mathematics Axiom of choice Discrete mathematics Zermelo–Fraenkel set theory Ring theory Ideal (ethics) Set (abstract data type) Set theory Law Geometry Commutative ring Computer science
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Topics
Rings, Modules, and Algebras
Physical Sciences → Mathematics → Algebra and Number Theory
Advanced Algebra and Logic
Physical Sciences → Computer Science → Computational Theory and Mathematics
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