Sentence examples for finite presentation from inspiring English sources

For a finitely presented semigroup, a Dehn function does not depend on the choice of finite presentation (up to equivalence), and the equivalence class of that function is called the Dehn function of the semigroup.

Let $R \to A$ be a ring map of finite presentation.

For example, for every hyperbolic group the word problem is solvable, and every hyperbolic group has a finite presentation.

Suppose that P = [ X ; r ] is a finite presentation for a monoid ℳ.

Then (langle S mid R cup R^{prime } rangle ) is a finite presentation of (G/N).

Depending on these numbers, we define χ ( G ) = min { χ ( P ) : P  is a finite presentation for  G }.

Appendix A: On soluble groups, metabelian groups, and finite presentations.

The 2.5D finite element presentation is employed here to describe the vibration of the rail.

With this background, we define the finite monoid presentation P to be efficient if χ ( P ) = δ ( M ), and we define the monoid ℳ to be efficient if it has an efficient presentation.

Recall that the Dehn function of a finite semigroup presentation (langle Xmid Rrangle ) is the minimal function f(n) such that for any words u, v which are equal in S and such that (|u|+|v|le n,) there exists a derivation of length at most f(n) of this equality from the defining relations.

In the following first subsection, as supportive material, some algebraic facts over split extensions (equivalently, semi-direct products), presentations of finite monogenic monoids, a trivializer set of these presentations and efficiency (equivalently, p-Cockcroft property) are reminded.