Open Access Journal

ISSN : 2456-1304 (Online)

International Journal of Engineering Research in Electronics and Communication Engineering(IJERECE)

Monthly Journal for Electronics and Communication Engineering

Open Access Journal

International Journal of Science Engineering and Management (IJSEM)

Monthly Journal for Science Engineering and Management

ISSN : 2456-1304 (Online)

Normality in Idempotent Commutative 𝛤-Semi group

Author : S. Suguna 1 D. Radha 2

Date of Publication :20th April 2018

Abstract: In this paper, a normality in an idempotent commutative 𝛤-semigroup is defined. A notion of left (right) normal, left (right) quasi-normal, regular, normal, left (right) semi-normal, left (right) semi-regular, in a normal idempotent commutative𝛤- semigroup S are defined. Any left (right) normal is left (right) quasi-normal in an idempotent commutative 𝛤-semigroup and vice versa. Also, it is regular if and only if it is normal and the same statement is proved with respect to semi-regular and semi-normal substructure. Any quasi-normal is also semi-regular as well as semi-normal and also the converse in an idempotent commutative 𝛤-semigroup. In a commutative idempotent 𝛤-semigroup, left regularity implies both left and right normality

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