Infinite global dimension for a product of fields

[skyscrapersheaf]

Let's describe a product of fields as a quotient of a quiver algebra by an inadmissible ideal:

LoadPackage("qpa");
Q:= Quiver(1,[[1,1,"a"]]);
kQ := PathAlgebra(Rationals,Q);
gens := GeneratorsOfAlgebra(kQ);
a:= gens[2];
relations:=[a^2-a];
I:=Ideal(kQ,relations);
A:=kQ/I;

Calling GlobalDimension(A) throws an error. However, calling GlobalDimensionOfAlgebra(A, 3) outputs infinity, and so does GlobalDimension(A) afterwards. A is just the algebra k/<a^2-a> which is isomorphic to a product of fields k x k with the basis a, 1-a and hence has global dimension 0.

[sunnyquiver]

Thank you for pointing out this. However, there is a lot of functions which would produce the wrong results when applied to quotients of path algebras by in-admissible ideals. Most of QPA is built for admissible quotients, while still accommodating the possibility to compute with quotient by in-admissible ideals. So, this dependence on admissible quotients should possibly be made more explicit. Another question is if one should introduce a check for an admissible quotient whenever it is required.