Apery Sets of Numerical Semigroups
Madero-Craven, Monica Grace
Washington, Larry C
Adams, William W
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A numerical semigroup is a subset, S of the non-negative integers, Z+ which contains zero, is closed under addition, and whose complement in Z+ is finite. We discuss the basic properties of numerical semigroups as well as associated structures such as relative ideals. Further, we examine several finite subsets of S including the Apery Set and two of its subsets. Relationships between these subsets of S will allow us to give an equivalent definition for S to be symmetric as well as a necessary condition for S to be almost symmetric.