Global determinism of semigroups having regular globals |
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Authors: | Aiping Gan Xianzhong Zhao Miaomiao Ren |
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Institution: | 1.Department of Mathematics,Northwest University,Xi’an,People’s Republic of China;2.College of Mathematics and Information Science,Jiangxi Normal University,Nanchang,People’s Republic of China |
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Abstract: | The aim of this paper is to study the global determinism of the class \({\mathcal {A}}\) of all semigroups having regular globals. It is known from PeliKán (Periodica Math Hungarica 4:103–106, 1973) and Pondělí?ek (On semigroups having regular globals, 1976) that \({\mathcal {A}}\) can be divided into two subclasses: the class \({\mathcal {A}}_{2}\) of all semigroups having idempotent globals and the class \({\mathcal {A}}_{3}\) of all semigroups having regular but non-idempotent globals. We prove that \({\mathcal {A}}_{2}\) is globally determined and that \({\mathcal {A}}_{3}\) satisfies the strong isomorphism property. This shows that \({\mathcal {A}}\) is globally determined. |
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