In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices...In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.展开更多
文摘In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.
