Zappa-Szép Products of Semigroups

• 作者: Suha Wazzan
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Inverse SEMIGROUPS Groups SEMILATTICE Rectangular Band Semidiret REGULAR ENLARGEMENT INDUCTIVE GROUPOID
• 年，卷（期）: 2015,（6）
• 页码范围: 1047-1068
• 页数: 22页
• 分类号: O1

摘要

The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.