Say and are both coprime to . Let be the lattice
.
What is the determinant of ? I think the answer may be that it's the cardinality of the subset of generated by and but I can't prove it. Is this a standard result?
Yes, means , but I'll write if it's confusing. And yes, the lattice is going to be an infinite set of points (and then the determinant is defined in the standard way - see eg. Lattice (group) - Wikipedia, the free encyclopedia )