Home Online Manual
Top
Back: triangularGroup
Forward: lpNoetherian
FastBack:
FastForward:
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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  compute the Gelfand Kirillov dimension of A/<GB>
7.10.3.5 lpGlDimBound  compute an upper bound for the global dimension of A/<GB>
7.10.3.6 lpSubstitute  substitute a variable with polynomials (ring homomorphism)
7.10.3.7 lpUfGraph  constructs the Ufnarovskij graph for <LM(GB)>
7.10.3.8 lpCalcSubstDegBound  utility for lpSubstitute
See also: fpadim_lib; freegb_lib.