Abstract
A semigroup is an algebraic structure which only involve one binary operation that is associative. Research on a semigroup has grown rapidly, included an ordered semigroup. An ordered semigroup is a semigroup that is added an ordered operation such that it meets some axioms. A bilinear forms semigroup is a semigroup whose the elements are adjoin ordered pairs relative to a bilinear form. In this study, we have investigated the properties of an ordered bilinear form semigroup based on its regular elements. We have obtained some properties associated with the biggest inverse element and the biggest idempotent element. The other results we investigated the properties of Right (Left) Green equivalence classes on the ordered bilinear form semigroup related to their biggest inverse element and the biggest idempotent element.
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