Abstract. In this paper, the concept of a medial idempotent is generalized, called a quasi-medial idempotent. After that, some properties about an abundant semigroup with a quasi-medial idempotent is studied. In particular, a structure theorem for an abundant semigroup with a quasi-medial idempotent is given and some special cases are considered.

Received: August 3, 2011

AMS Subject Classification: 20M10

Key Words and Phrases: abundant semigroup, quasi-medial idempotent, weak medial idempotent, medial idempotent

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