Leonid Monin, Department of Mathematics, University of Toronto, Toronto, ON Canada M5S 2E4 e-mail: lmonin@math.toronto.edu

Abstract/Résumé:

In this paper the geometry of the lattice is used to prove basic theorems about subgroups and factor groups of \(\Bbb Z^n\). We suggest a geometric algorithm which reduces a finitely generated abelian group to its normal form.

Dans ce papier, un argument de géométrie sur les réseaux est utilisé pour prouver des théorèmes fondamentaux sur les sous-groupes ou les groupes quotients de \(\Bbb Z^n\). Nous proposons un algorithme géométrique qui réduit un groupe abélien finement engendré à sa forme normale.

Keywords: Integer lattice, Integer volume, Normal Smith form

AMS Subject Classification: Lattice polytopes (including relations with commutative algebra and algebraic geometry) 52B20

PDF(click to download): Lattice Geometry and Reduction of Finitely Generated Abelian Groups to a Normal Form

R.M. Erdahl

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Quadratic forms (reduction theory; extreme forms; etc.), Lattice polytopes (including relations with commutative algebra and algebraic geometry), , Tilings in $n$ dimensions 11H55, 52B20, 52B30, 52C22

PDF(click to download): Space filling zonotopes and Voronoi's conjecture on parallelohedra