Singular

7.10.3 fpaprops_lib

Library:

fpaprops.lib

Purpose:

Algorithmic ring-theoretic properties of finitely presented algebras (Letterplace)

Authors:

Karim Abou Zeid, karim.abou.zeid at rwth-aachen.de

Support: Project II.6 in the transregional collaborative research centre SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German DFG

Overview:

In this library, algorithms for computing various ring-theoretic properties of finitely presented algebras are implemented.
Applicability: Letterplace rings.

References:

Huishi Li: Groebner bases in ring theory. World Scientific, 2010.

Procedures:

7.10.3.1 lpNoetherian		check whether A/<LM(GB)> is (left/right) Noetherian
7.10.3.2 lpIsSemiPrime		check whether A/<LM(GB)> is semi-prime
7.10.3.3 lpIsPrime		check whether A/<LM(GB)> is prime
7.10.3.4 lpGkDim		alias for dim(<GB>)
7.10.3.5 teach_lpGkDim		deprecated, kept for teaching purposes. use dim(<GB>) instead.
7.10.3.6 lpGlDimBound		compute an upper bound for the global dimension of A/<GB>
7.10.3.7 lpSubstitute		substitute a variable with polynomials (ring homomorphism)
7.10.3.8 lpCalcSubstDegBound		utility for lpSubstitute