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The American Mathematical Monthly Volume 118, 2011 - Issue 10
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Articles

Factorizations of Algebraic Integers, Block Monoids, and Additive Number Theory

Paul BaginskiInstitut Camille Jordan, Université Claude Bernard Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne, [email protected]View further author information
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Scott T. ChapmanDepartment of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, [email protected]View further author information
Pages 901-920 | Published online: 13 Dec 2017

Citations (17)

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Read on this site (9)

Nicholas R. Baeth & Scott T. Chapman. (2023) The Importance of Being Prime⋆, a Nontrivial Generalization for Nonunique Factorizations. The American Mathematical Monthly 130:10, pages 893-914.
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Stephan Ramon Garcia, Christopher O'Neill & Gabe Udell. (2022) Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups. Communications in Algebra 50:8, pages 3481-3497.
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Jackson Autry, Tara Gomes, Christopher O’Neill & Vadim Ponomarenko. (2020) Elasticity in Apéry Sets. The American Mathematical Monthly 127:8, pages 744-749.
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Scott T. Chapman. (2019) So What Is Class Number 2?. The American Mathematical Monthly 126:4, pages 330-339.
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Alfred Geroldinger. (2016) Sets of Lengths. The American Mathematical Monthly 123:10, pages 960-988.
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Paul Baginski, Ryan Rodriguez, George J. Schaeffer & Yiwei She. (2016) Finding Elements With Given Factorization Lengths and Multiplicities. The American Mathematical Monthly 123:9, pages 849-870.
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Christopher O'Neill & Roberto Pelayo. (2015) How Do You Measure Primality?. The American Mathematical Monthly 122:2, pages 121-137.
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Matthew Jenssen, Daniel Montealegre & Vadim Ponomarenko. (2013) Irreducible Factorization Lengths and the Elasticity Problem within ℕ. The American Mathematical Monthly 120:4, pages 322-328.
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Nicholas R. Baeth & Roger Wiegand. (2013) Factorization Theory and Decompositions of Modules. The American Mathematical Monthly 120:1, pages 3-34.
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Articles from other publishers (8)

Austin A. Antoniou & Salvatore Tringali. (2021) On the arithmetic of power monoids and sumsets in cyclic groups. Pacific Journal of Mathematics 312:2, pages 279-308.
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Stephan Ramon Garcia, Mohamed Omar, Christopher O'Neill & Samuel Yih. (2021) Factorization length distribution for affine semigroups II: Asymptotic behavior for numerical semigroups with arbitrarily many generators. Journal of Combinatorial Theory, Series A 178, pages 105358.
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Yushuang Fan & Salvatore Tringali. (2018) Power monoids: A bridge between factorization theory and arithmetic combinatorics. Journal of Algebra 512, pages 252-294.
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Bumsoo Kim. (2015) The cross number of minimal zero-sum sequences in finite abelian groups. Journal of Number Theory 157, pages 99-122.
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Xiaoyu He. (2014) Cross number invariants of finite abelian groups. Journal of Number Theory 136, pages 100-117.
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Paul Baginski & Scott Chapman. 2014. Combinatorial and Additive Number Theory. Combinatorial and Additive Number Theory 15 38 .
Daniel Kriz. (2013) On a conjecture concerning the maximal cross number of unique factorization indexed sequences. Journal of Number Theory 133:9, pages 3033-3056.
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Alfred Geroldinger & David J. Grynkiewicz. (2013) The large Davenport constant I: Groups with a cyclic, index subgroup . Journal of Pure and Applied Algebra 217:5, pages 863-885.
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