逆半群による帯の正則拡大について

This is a supplement to the previous papers [8], [9] and [10] . In [8], [9] and [10], the concept of a complete regular product S of a band B and an inverse semigroup Γ, and the concept of a half-direct product T of a left regular band E, an inverse semigroup Γ' and a right regular band F were introduced. In this paper, we first show that a semigroup M is inversive [quasi-(C)-inversive] if and only if M is isomorphic to a complete regular product of a band and a weakly C-inversive semigroup [a half-direct product of a left regular band, a weakny C-inversive semigroup and a right regular band] . If in particular Γ and Γ' are weakly C-inversive, both the spined product of B, Γ and that of E, Γ', F can be considered. When Γ [Γ'] is weakly C-inversive, we investigate the relationship between the complete regular products of B, Γ and the spined product of B, Γ [the half-direct products of E, Γ', F and the spined product of E, Γ', F].