Natural congruences and isomorphism theorems for directed complete partially ordered sets

详细信息    查看全文

• 作者：Mojgan Mahmoudi ; Halimeh Moghbeli ; Konrad Pióro
• 关键词：2010 Mathematics Subject ClassificationPrimary ; 06A11 ; Secondary ; 06B10 ; 06F99 ; 08A02 ; 08A30 ; 18A32
• 刊名：Algebra universalis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：77
• 期：1
• 页码：79-99
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Springer International Publishing
• ISSN：1420-8911
• 卷排序：77

文摘

Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural congruences of dcpos. We also show that the kernels of dcpo maps, that is, directed join-preserving maps between dcpos are not necessarily natural dcpo congruences. Then we characterise dcpo maps whose kernels are natural dcpo congruences. Finally, we prove the Decomposition and Isomorphism Theorems for dcpo maps.