[GAP Forum] Re: Test for maximality

[Alexander Hulpke]

Dear Forum,

S.Kolte asked:

> Is there a program in gap to test wether or not a given ideal is  
> maximal?

For arbitrary rings I would assume this to be unsolvable.

For multivariate polynomial rings this can be determined using  
Gr"obner basis theory, but the concrete method is not implemented in  
GAP, you might want to look at Singular.

If the ring is a finite dimensional algebra, GAP can test whether the  
quotient ring is simple.

Best,

    Alexander Hulpke