The Transcendence Degree over a Ring

Details The Transcendence Degree over a Ring The Transcendence Degree over a Ring

2011-09-07

arxiv.org/abs/1109.1391v1

Mathematics

Commutative Algebra

Scientific paper

For a finitely generated algebra over a field, the transcendence degree is known to be equal to the Krull dimension. The aim of this paper is to generalize this result to algebras over rings. A new definition of the transcendence degree of an algebra A over a ring R is given by calling elements of A algebraically dependent if they satisfy an algebraic equation over R whose trailing coefficient, with respect to some monomial ordering, is 1. The main result is that for a finitely generated algebra over a Noetherian Jacobson ring, the transcendence degree is equal to the Krull dimension.

Affiliated with

Also associated with

No associations

Rating

The Transcendence Degree over a Ring does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Transcendence Degree over a Ring, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Transcendence Degree over a Ring will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-305887