On some specific results of rings with prime nilradical

Abstract

The authors of A. Benhissi and S. Hizem [Nonnil-Noetherian rings and SFT property, Rocky Mountain J. Math. 41 (2011) 1483–1500] proved that the primary decomposition of a nonnil-ideal of a nonnil-Noetherian ring always exists. We will show in this paper that this primary decomposition is minimal. We next prove that over any nonnil-Noetherian ring, a sub-class of modules admit a primary decomposition. In the second part of this paper, we give some properties related to [Formula: see text]-chained and [Formula: see text]-Prüfer rings.