A Noncommutative Semigroup which Contains the Natural Numbers under Addition and Its Left Ideals

Ekkachai  Laysirikul; Kitsanachai  Sripon

Authors

Ekkachai Laysirikul Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000
Kitsanachai Sripon Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000

Keywords:

Semigroup, Subsemigroup, Left ideal, Right ideal, Isomorphism

Abstract

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.

References

Backelin, J. (1990). On the number of semigroups of natural numbers. Mathematica Scandinavica, 66, 197-215.

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.