Abstract
In this paper, we study the structure of E-unitary inverse semigroups together with related classes such as proper left ample semigroups and proper left restriction semigroups. Important theorems on proper left ample semigroups and proper left restriction semigroups analogous to the P-theorem for E-unitary inverse semigroups are considered. From these theorems, we obtain a structure theorem for proper inverse semigroups.
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