| $\Sigma$-Associated Primes over Extension Rings |
| Received:August 31, 2014 Revised:November 22, 2014 |
| Key Words:
associated prime Ore extension $\Sigma$-associated prime
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071062) and the Scientific Research Fundation of Hunan Provincial Education Department (Grant No.12B101). |
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| Abstract: |
| In this paper we introduce a concept, called $\Sigma$-associated primes, that is a generalization of both associated primes and nilpotent associated primes. We first observe the basic properties of $\Sigma$-associated primes and construct typical examples. We next describe all $\Sigma$-associated primes of the Ore extension $R[x;\alpha,\delta]$, the skew Laurent polynomial ring $R[x,x^{-1};\alpha]$ and the skew power series ring $R[[x;\alpha]]$, in terms of the $\Sigma$-associated primes of $R$ in a very straightforward way. Consequently several known results relating to associated primes and nilpotent associated primes are extended to a more general setting. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.05.004 |
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