A point model for the free cyclic submodules over ternions
Hans Havlicek, Boris Odehnal, Jaroslaw Kosiorek
TL;DR
This paper introduces a geometric model for all free cyclic submodules of T^2 over the ring of ternions, unifying unimodular and non-unimodular cases within a smooth algebraic variety.
Contribution
It provides the first algebraic variety model for free cyclic submodules over ternions, extending geometric understanding in module theory.
Findings
Unified geometric model for free cyclic submodules
Representation of unimodular and non-unimodular cases
Connection between module theory and algebraic geometry
Abstract
We show that the set of all (unimodular and non-unimodular) free cyclic submodules of T^2, where T is the ring of ternions over a commutative field, admits a point model in terms of a smooth algebraic variety.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry