GENERALIZED PRIMARY RINGS

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.

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  • Department of Mathematics, Computer Science, and Statistics McNeese State University Lake Charles, Louisiana, 70609 e-mail: cgorton@mcneese.edu Henry E. Heatherly
  • Department of Mathematics University of Louisiana at Lafayette Lafayette, Louisiana, 70504-1010 e-mail: heh5820@louisiana.edu Ralph P. Tucci
  • Department of Mathematical Sciences Loyola University New Orleans New Orleans, Louisiana, 70118 e-mail: tucci@loyno.edu