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The Inverse Semigroup Extension of Clifford Semigroup

Zhu Wen

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Abstract

Extending a given semigroup is one of the main methods to construct a new semigroup.In this paper,the inverse semigroup extension of a Clifford semigroup is discussed.The concept of full inverse semigroup is introduced and the properties of Green relation between full inverse semigroups are presented.The definition of inverse semigroup extension of Clifford semigroup is given and debated.

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What this paper is about

Extending a given semigroup is one of the main methods to construct a new semigroup.In this paper,the inverse semigroup extension of a Clifford semigroup is discussed.The concept of full inverse semigroup is introduced and the properties of Green relation between full inverse semigroups are presented.The definition of inverse semigroup extension of Clifford semigroup is given and debated.

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Available abstract

Extending a given semigroup is one of the main methods to construct a new semigroup.In this paper,the inverse semigroup extension of a Clifford semigroup is discussed.The concept of full inverse semigroup is introduced and the properties of Green relation between full inverse semigroups are presented.The definition of inverse semigroup extension of Clifford semigroup is given and debated.

Key concepts: Semigroup, Bicyclic semigroup, Inverse semigroup, Mathematics, Extension (predicate logic), Cancellative semigroup, Inverse element, Inverse

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