Extension of cancelable commutative semigroups
Zhaoying Chen, Xiu Qing Wang · 2022
In this paper, an important conclusion which every cancelable Abelian semigroup is a subsemigroup of an Abelian group is characterized in detail, and all positive rational numbers Q+ is an Abelian group containing N made up all natural numbers which forms a cancelable commutative semigroup for ordinary multiplication, in the following, we deduce a fractional group is the smallest Abelian group containing a cancelable Abelian semigroup. In the end, an important relation between outer direct product of fractional groups and cancelable commutative semigroups is established.