Applications of Homomorphism on the Structure of Semigroups

• 作者: Huishu Yuan Xiangzhi Kong
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: HOMOMORPHISM Natural PARTIAL Order Green’s (* ~) -Relation SEMILATTICE DECOMPOSITION
• 年，卷（期）: 2014,（2）
• 页码范围: 62-70
• 页数: 9页
• 分类号: O1

摘要

By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,~-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.