Dergiler / International Electronic Journal of Algebra / 2012 / Cilt: 12 - Sayı: 12

GENERALIZED PRIMARY RINGS

Christine GORTON, Henry E. HEATHERLY, Ralph P. TUCCİ

Sayfa
116–132
DOI
—

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.