. A -semigroup is generalization from semigroup, which concepts in -semigroup analogue with concepts in semigroup. is called a -semigroup if there is a mapping between two nonempty sets and , written as , such that , for all and . A -semigroup is said to be intra-regular if contains for all elements of intra regular, is if , for all and . In this paper, discussed about intra-regular -semigroup and the relation based on bi-ideals, quasi-ideals, and ideals right and left.
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