Arf semigroup
Encyclopedia
In mathematics, Arf semigroups are certain subsets of the positive integer
s closed under addition
, that were studied by . They appeared as the semigroups of values of Arf ring
s.
A subsemigroup of the positive integers, with elements ρ1 < ρ2 < ρ3 ..., is called an Arf semigroup if it contains ρi + ρj − ρk whenever i≥j≥k.
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s closed under addition
Addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
, that were studied by . They appeared as the semigroups of values of Arf ring
Arf ring
In mathematics, an Arf ring was defined by to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied by ....
s.
A subsemigroup of the positive integers, with elements ρ1 < ρ2 < ρ3 ..., is called an Arf semigroup if it contains ρi + ρj − ρk whenever i≥j≥k.