Date of Publication :20th April 2018
Abstract: In this paper, a normality in an idempotent commutative ð›¤-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 commutativeð›¤- semigroup S are defined. Any left (right) normal is left (right) quasi-normal in an idempotent commutative ð›¤-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 ð›¤-semigroup. In a commutative idempotent ð›¤-semigroup, left regularity implies both left and right normality
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