COMMUTATIVE RINGS IN WHICH EVERY PRINCIPAL IDEAL IS A FINITE INTERSECTION OF PRIME POWER IDEALS

Abstract

In this paper we establish several equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of prime power ideals to be a general ZPI-ring. Using these results, we establish some equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of primary ideals to be a general ZPI-ring.

Keywords:

• General ZPI-ring
• Multiplication ring
• C-prime ideal
• Strong C-prime ideal
• 1991 Mathematics Subject Classification: 13A15, 13F20, 13G05

ACKNOWLEDGMENT

The author would like to thank the referee for his helpful comments and suggestions.