• NONNIL-NOETHERIAN COMMUTATIVE RINGS AND NONNIL IDEALS

Abstract

In this paper, it should be noted that a commutative ring R is said to be Nonnil-Noetherian if every Nonnil Ideal of R is finitely generated. A ring R is said to be Nonnil-Noetherian if R is both right and left Nonnil-Noetherian ring. In the first section of this paper we show that many of the properties Noetherian rings are also true for Nonnil-Noetherian rings. In the second section we show that the direct sum of Nonnil-Noetherian ring needs not to be Noetherian.