GENERALIZED PRIMARY RINGS

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