Determining cyclicity of finite modules
H. W. Lenstra Jr., A. Silverberg
TL;DR
This paper introduces a deterministic polynomial-time algorithm to decide if a finite module over a finite commutative ring is cyclic and to find a generator if it exists.
Contribution
It provides the first efficient algorithm for determining cyclicity of modules over finite commutative rings.
Findings
Algorithm runs in polynomial time
Successfully identifies generators for cyclic modules
Applicable to a broad class of finite modules
Abstract
We present a deterministic polynomial-time algorithm that determines whether a finite module over a finite commutative ring is cyclic, and if it is, outputs a generator.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Logic, programming, and type systems