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A Note on Finitely Generated Modules over a <i>PID</i>
Department of Mathematics, Shanghai University, Shanghai, China
School of Mathematics and Statistics, Hubei University, Wuhan, China
Department of Mathematics, Shanghai University, Shanghai, China
- 1 Department of Mathematics, Shanghai University, Shanghai, China
- 2 School of Mathematics and Statistics, Hubei University, Wuhan, China
- 3 Department of Mathematics, Shanghai University, Shanghai, China
Advances in Pure Mathematics·Volume 10 (2020)·Pages 699–705·Published 3 December 2020·DOI10.4236/apm.2020.1012043
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Abstract
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
KeywordsFinitely Generated ModulePrincipal Ideal DomainCyclic Module
- Hungerford, T.W. (1974) Algebra. Springer-Verlag, New York.
- Jacobson, N. (1985) Basic Algebra I. W. H. Freman and Company, New York.
- Jacobson, N. (1953) Lectures in Abstract Algebra II. Linear Algebra. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4684-7053-6
- Geroldinger, A. and Schwab, E.D. (2017) Sets of Lengths in Atomic Unit-Cancellative Finitely Presented Monoids. Colloquium Mathematicum, 151, 171-187. https://doi.org/10.4064/cm7242-6-2017