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On (*, ∼)-Green's Relations and Ortho-lc-Monoids

An ortho-lc-monoid is a generalized orthogroup within the class of rpp semigroups. In this article, after giving some important properties of r-ample semigroups and super-r-ample semigroups, some structure theorems of ortho-lc-monoids are established, and several special cases are considered. The main techniques that we use in the study are the (*, ∼)-Green's relations and semispined product of semigroups.