University of KashanMathematics Interdisciplinary Research2538-36393220181201Classification of Monogenic Ternary Semigroups1391468843610.22052/mir.2019.173544.1120ENNahidAshrafiFaculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, IranZahraYazdanmehrFaculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, IranJournal Article20180302The aim of this paper is to classify all monogenic ternary semigroups,<br /> up to isomorphism. We divide them to two groups: finite and infinite.<br /> We show that every infinite monogenic ternary semigroup is isomorphic to<br /> the ternary semigroup O, the odd positive integers with ordinary addition.<br /> Then we prove that all finite monogenic ternary semigroups with the same<br /> index and the same period are isomorphic. We also investigate structure of<br /> finite monogenic ternary semigroups and we prove that any finite monogenic<br /> ternary semigroup is isomorphic to a quotient ternary semigroup.http://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdf