| Graded Excellent Extensions of Graded Rings |
| Received:June 07, 2005 Revised:July 02, 2006 |
| Key Words:
graded excellent extension graded right $V$-ring graded $PS$-ring graded Von Neumann regular ring.
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| Fund Project:the National Natural Science Foundation of China (10471055); the Scientific Research Foundation of Liaoning Education Department (05L014). |
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| Abstract: |
| The concept of graded excellent extension of graded rings is introduced. Let $S=\bigoplus_{g\in G}S_g$ be a graded excellent extension of $R=\bigoplus_{g\in G}R_g$. We prove that $S$ is a graded right $V$-ring if and only if $R$ is a graded right $V$-ring, $S$ is graded $PS$-ring if and only if $R$ is a graded $PS$-ring, and $S$ is a Von Neumann regular ring if and only if $R$ is a graded Von Neumann regular ring. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.03.018 |
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