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Titlebook: Numerical Semigroups; J.C. Rosales,P. A. García-Sánchez Book 2009 Springer Science+Business Media, LLC 2009 Additive Semigroups.Embedding

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发表于 2025-3-21 17:32:51 | 显示全部楼层 |阅读模式
书目名称Numerical Semigroups
编辑J.C. Rosales,P. A. García-Sánchez
视频videohttp://file.papertrans.cn/670/669168/669168.mp4
概述First monograph devoted exclusively to the study of numerical semigroups.Presents various applications of numerical semigroups including number theory, coding theory, algebraic geometry, and others.Th
丛书名称Developments in Mathematics
图书封面Titlebook: Numerical Semigroups;  J.C. Rosales,P. A. García-Sánchez Book 2009 Springer Science+Business Media, LLC 2009 Additive Semigroups.Embedding
描述Let N be the set of nonnegative integers. A numerical semigroup is a nonempty subset S of N that is closed under addition, contains the zero element, and whose complement in N is ?nite. If n ,...,n are positive integers with gcd{n ,...,n } = 1, then the set hn ,..., 1 e 1 e 1 n i = {? n +··· + ? n | ? ,...,? ? N} is a numerical semigroup. Every numer e 1 1 e e 1 e ical semigroup is of this form. The simplicity of this concept makes it possible to state problems that are easy to understand but whose resolution is far from being trivial. This fact attracted several mathematicians like Frobenius and Sylvester at the end of the 19th century. This is how for instance the Frobenius problem arose, concerned with ?nding a formula depending on n ,...,n for the largest integer not belonging to hn ,...,n i (see [52] 1 e 1 e for a nice state of the art on this problem).
出版日期Book 2009
关键词Additive Semigroups; Embedding Dimension; Frobenius Number; Group theory; Irreducible; Modular; Monoid; Num
版次1
doihttps://doi.org/10.1007/978-1-4419-0160-6
isbn_softcover978-1-4614-2456-7
isbn_ebook978-1-4419-0160-6Series ISSN 1389-2177 Series E-ISSN 2197-795X
issn_series 1389-2177
copyrightSpringer Science+Business Media, LLC 2009
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发表于 2025-3-21 22:10:01 | 显示全部楼层
Numerical semigroups with maximal embedding dimension,they have become specially renowned due to the existing applications to commutative algebra via their associated semigroup ring (see for instance [1, 5, 15, 16, 99, 100]). They are a source of examples of commutative rings with some maximal properties. As we mentioned in the introduction of Chapter
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Irreducible numerical semigroups, these semigroups is due mainly to Kunz, who in his manuscript [44] proves that a onedimensional analytically irreducible Noetherian local ring is Gorenstein if and only if its value semigroup is symmetric. Symmetric numerical semigroups always have odd Frobenius number. The translation of this conc
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Presentations of a numerical semigroup,e fact that every finitely generated (commutative) monoid is finitely presented. Rédei’s proof is long and elaborated. Many other authors have given alternative and much simpler proofs than his (see for instance [31, 39, 41, 56]). Since numerical semigroups are cancellative monoids, a different appr
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Numerical semigroups with embedding dimension three,h the help of Proposition 1.17 and what we know about embedding dimension two numerical semigroups, a formula for the Frobenius number and the genus of a symmetric numerical semigroup with embedding dimension three can easily be found. As for the pseudo-symmetric case, an expression for the Frobeniu
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Book 2009and Sylvester at the end of the 19th century. This is how for instance the Frobenius problem arose, concerned with ?nding a formula depending on n ,...,n for the largest integer not belonging to hn ,...,n i (see [52] 1 e 1 e for a nice state of the art on this problem).
发表于 2025-3-23 06:33:06 | 显示全部楼层
1389-2177 ber theory, coding theory, algebraic geometry, and others.ThLet N be the set of nonnegative integers. A numerical semigroup is a nonempty subset S of N that is closed under addition, contains the zero element, and whose complement in N is ?nite. If n ,...,n are positive integers with gcd{n ,...,n }
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