Classification of Monogenic Ternary Semigroups

Document Type : Original Scientific Paper

Authors

Faculty of Mathematics, Statistics and Computer Science Semnan University Semnan, Iran

Abstract

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index and the same period are isomorphic. We also investigate structure of finite monogenic ternary semigroups and we prove that any finite monogenic ternary semigroup is isomorphic to a quotient ternary semigroup.

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References

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Mathematics Interdisciplinary Research
Volume 3, Issue 2
December 2018
Pages 139-146

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