GENERALIZED PRIMARY RINGS

Year 2012, Volume: 12 Issue: 12, 116 - 132, 01.12.2012

Christine Gorton Henry E. Heatherly Ralph P. Tucci

Abstract

The Lasker-Noether concept of a primary ideal is extended in
various ways to the category of associative, not necessarily commutative rings.
Generically these are called generalized primary conditions (right and left).
The structure of generalized primary rings is developed. Special consideration
is given to these rings under various chain conditions. The additive structure
of such rings is addressed in detail. Examples are given to illustrate and delimit
the theory developed.

Keywords

generalized primary conditions, nilpotent ideals, principal ideals, radicals, chain conditions

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• Department of Mathematics, Computer Science, and Statistics McNeese State University Lake Charles, Louisiana, 70609 e-mail: [e-mail] Henry E. Heatherly
• Department of Mathematics University of Louisiana at Lafayette Lafayette, Louisiana, 70504-1010 e-mail: [e-mail] Ralph P. Tucci
• Department of Mathematical Sciences Loyola University New Orleans New Orleans, Louisiana, 70118 e-mail: [e-mail]