| A Note on Pseudo Primary Rings |
| Received:June 28, 1993 |
| Key Words:
primary ideal commutative ring.
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| Fund Project:Project Supported by the Natural Science Foundation of Liaoning Province. |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1995.03.004 |
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