Rational lattice

Proper sublattice

Let be a rational lattice an suppose is a proper sublattice, and has exponent . Then geo

and there exists

for integers not all equal to zero.¹

Proof

If has exponent , then , and thus . Moreover

forms a set of coset representatives for .

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Footnotes

1. 2022. Algebraic number theory course notes, ¶2.5, p. 35 ↩