Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
Can you give some context? It may be just a sinonym for 'most elements' or 'all elements'. – Berci Nov 2 '12 at 15:08
Is there a topology on the ring? – Dennis Gulko Nov 2 '12 at 15:13
Maybe a non-zero non-unit? – Your Ad Here Nov 2 '12 at 15:13
There seems to be a specialized meaning of generic element as described in this paper, Integral Closure and Generic Elements. 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 $R$. – hardmath Nov 2 '12 at 15:32
What an unfortunate choice of terminology. Not as bad as defining a special meaning for "arbitrary element," but close! – rschwieb Nov 2 '12 at 17:33

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.