Abstract

We call a quasi-adequate semi-group whose set of idempotents forms a left [right] quasi-normal band a left [right] semi-perfect abundant semi-group. After obtaining some characterization theorems of such quasi-adequate semi-groups, we establish a structure for left [right] semi-perfect abundant semi-groups of type W. Our results generalize and strengthen the results of El-Qallali and Fountain on quasi-adequate semi-groups.

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