摘 要：本文研究了重数为5 的数字半群的不可约性。通过计算数字半群的亏格和Frobenius 数，刻画了重数为5 的数字半群的特点，分析了重数为5 的不可约数字半群和5- 不可约数字半群之间的关系，进而确定了哪些重数为5 的不可约数字半群也是5- 不可约数字半群。最后对重数为5 的数字半群，通过分类列表整理的形式，分别列出嵌入维数为3、4 和5 的数字半群，对其不可约性和5- 不可约性的关系进行了初步研究。
关键词：数字半群；不可约；Frobenius 数；亏格
中图分类号：O152.7 文献标识码：A 文章编号：2096-4706（2019）14-0013-05
Irreducible Numerical Semigroup with Multiplicity 5
LING Yan，SUN Guangren
（School of Mathematics and Computational Sciences，Anqing Normal University，Anqing 246133，China）
Abstract：In this paper，we study the irreducibility of digital semigroups with multiplicity 5. And completely describes the characteristics of the numerical semigroup with the multiplicity and analyzed the relationship between the irreducible numerical semigroup with the multiplicity of 5 and the 5- irreducible numerical semigroup by calculating the genus of the numerical semigroup and the Frobenius number. Furthermore，it is determined which irreducible numerical semigroups with multiplicity 5 are also irreducible numerical semigroups with multiplicity 5-. Finally，we list the numerical semigroups with embedding dimensions of 3，4 and 5 separately by the classification list for the numerical semigroup with a multiplicity of 5，and then the relationship between the 5 irreducibility and the 5-reducibility is studied.
Keywords：numerical semigroups；irreducible；Frobenius number；genus
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作者简介：凌燕（1992-），女，汉族，安徽池州人，硕士研究生，研究方向：应用数学。