In this paper, we introduce a new semigroup which is not commutative. Then we investigate some properties in this structure. We discover that this semigroup has no a proper right ideal. After that we find some subsemigroups of this semigroup which are left ideals. Finally, we prove that the natural numbers under addition can be embedded into this semigroup.
Barucci, V. (2009). On propinquity of numerical semigroups and one-dimensional local Cohen Macaulay rings. Proceedings of Fifth International Fez Conference on Commutative Algebra and applications. 49-60.