Sentence examples for finite over from inspiring English sources

By Lemma 9.16.3 this is the normal closure of $M/K$ and is finite over $K$.

The algebraic closure of $k$ in $K$ is finite over $k$.

We can choose a subring $A_0 \subset A$ which is a regular complete local ring such that $A$ is finite over $A_0$, see Algebra, Lemma 10.154.11.

Thus, we conclude that if a system is linear, stable, and causal and if the impedance is finite over the frequency domain, the impedance data will transform according to the K K relationships.

Since R i is finite over the noetherian ring A i, it is noetherian as well.

J → 2 Ω Open image in new window is finite over the cross section π rc2 of a nanotube and zero over the area a2 = 1/N (where a is the separation between the nanotubes).

However, provably correct but conservative approaches, in which the satisfaction of a property by a dynamical system is implied by the satisfaction of the property by a finite over-approximation (abstraction) of the system, have received a lot of attention in recent years.

I am especially interested in the geometry of algebraic curves, surfaces, threefolds and fourfolds over the complex numbers, over numbers fields, over finite fields, over fields of transcendence degree one over finite fields and over discrete valuation rings with perfect residue field.

The codes constructed include optimal, near-optimal self-orthogonal and self-dual codes, over finite fields and over Z4.

Simple finite algebras over a field are matrix algebras over a skew field.

Suggested slogan: Simple finite algebras over a field are matrix algebras over a skew field.