### 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.

User manual for Singular version 4.4.1, 2025, generated by texi2html.