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

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Ekkachai Laysirikul and Kitsanachai Sripon

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.

Keywords
Semigroup, Subsemigroup, Left ideal, Right ideal, Isomorphism
Section
Research Articles

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How to Cite
AND KITSANACHAI SRIPON, Ekkachai Laysirikul. A Noncommutative Semigroup which Contains the Natural Numbers under Addition and Its Left Ideals. Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 25, n. 2, p. 51-58, may 2017. ISSN 2539-553X. Available at: <http://www.journal.nu.ac.th/NUJST/article/view/1778>. Date accessed: 19 apr. 2019.