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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.