A Note on Pseudo Primary Rings

Abstract:

      A commutative ring with identity R is called a pseudo primary ring if eachnon-zero ideal of R is a power of a primary ideal. In this note we prove that a ring Ris a pseudo primary ring if and only if R is a primary ring or R is a direct sum of twofields or R is a one-dimensional local ring with at most three prime ideals in which eachnon-zero ideal is a power of a minimal prime ideal or is a power of some primary idealbelonging to the maximal ideal.