Terminology for the natural field associated to a prime ideal Consider a commutative ring R with a prime ideal P.
Is there a terminology or name for the field of fractions of the R/P in the literature? I suspect that "function field of P" is not a correct term.
My second question is there any standard (or at least widely used) notation for this field in the literature?

This is usually called the "residue field" at $P$, and is often denoted $k(P)$.  Both the term and the notation are also used more generally for the corresponding notion when $P$ is a point in a scheme (or more generally a locally ringed space).
