Affiliation:
1. ShangHai University of Finance & Economics ZheJiang College
2. Department of Mathematics, Zhejiang Normal University
Abstract
A weak normal idempotent of an abundant semigroup was introduced by Guo [7].
In this paper, weak normal idempotents and normal idempotents of abundant
semigroups are respectively characterized in many different ways. These
results enable us to obtain an example which shows that the class of normal
idempotents of abundant semigroups is a proper subclass of normal
idempotents of abundant semigroups. Furthermore, this example tell us that
there exists a non-regular abundant semigroup containing a weak normal
idempotent. At last, we investigate the relationships between weak normal
idempotents and normal idempotents and deduce that the main result of [2]
can not be generalized into the class of abundant semigroups.
Publisher
National Library of Serbia