Singular Manual: fpaprops_lib

> | ### 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
See also: fpadim_lib; freegb_lib.

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