International Journal of Science , Engineering and Management (IJSEM)

Monthly Journal for Science , Engineering and Management

Volume3,April 2018,

Topic : Normality in Idempotent Commutative 𝛤-Semi group

Authors: S. Suguna || D. Radha

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..

Keywords: 𝛤-semigroup, idempotent, commutative, left and right regular, left and right normal, left and right quasi-normal, left and right semi-normal, left and right semi-regular.

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DOI: 01.1617/vol5/iss4/pid54613


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Dr.Muhammad Ishtiaq,
Mirpur University of
Science & Technology,
Mirpur, Azad Kasmir.

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IMPACT FACTOR: 2.7

ISSN(Online): 2456-1304

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Thomson Reuters ID : q-6288-2016.
ORCiD Research ID : 0000-0001-9540-6799

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Journal Code : IJSEM
Electronic ISSN : 2456-1304
Impact Factor : 2.7
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