Abstract : In this paper, we first introduce the concept of left strongly simple $po$-semigroups, then we discuss properties and characterizations nil-extensions of left strongly simple $po$-semigroups and semilattices of left strongly simple $po$-semigroups. Finally, we give some characterizations of the chain of left strongly simple $po$-semigroups.
Keywords : left semiregular, left $\pi$-semiregular, left strongly simple, nil-extension, semilattices, chain
