[01] Chunhua Li, School of Science, East China Jiaotong University, Nanchang, Jiangxi, China. [02] Baogen Xu, School of Science, East China Jiaotong University, Nanchang, Jiangxi, China.

In this paper, we will investigate the natural partial orders on IC-abundant semigroups. After giving some properties and characterizations of natural partial orders on abundant semigroups, we consider IC-abundant semigroups. We prove that an IC-abundant semigroup is locally ample if and only if the natural partial order on the semigroup is compatible with the multiplication.

Abundant Semigroup, Natural Partial Order, IC-Abundant Semigroup, Locally Ample

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