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I am now reading a commutative algebra paper, in which the name "generic element" of a commutative ring appears, however, I can not find the definition in that paper, and also my commutative algebra textbook.

So, could you please tell me what is a generic element in a commutative ring ? Where can I find its definition and related property ? What is it useful for ?

Thank for reading my question !

Edit That paper is a survey on Castelnuovo-Mumford regularity and was written by Le Tuan Hoa. It firstly appear in the lemma 1.3.

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    Can you give some context? It may be just a sinonym for 'most elements' or 'all elements'.2012-11-02
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    Is there a topology on the ring?2012-11-02
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    Maybe a non-zero non-unit?2012-11-02
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    There seems to be a specialized meaning of *generic element* as described in this paper, [Integral Closure and Generic Elements](http://www.ndsu.edu/pubweb/~ciuperca/generic-final.pdf). It appears that for ring $R$, a generic element is identified with a linear combination of generators $X_i$ for polynomial ring $R[X_1,..,X_n]$, i.e. a generic point in a multivariate extension of ring $R$.2012-11-02
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    What an unfortunate choice of terminology. Not as bad as defining a special meaning for "arbitrary element," but close!2012-11-02
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    I thought generic point always refers to elements of Spec(R). Have you thought about contacting the author?2012-11-02

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