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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (5): 512-516    DOI: 10.3785/j.issn.1008-9497.2016.05.002
数学与计算机科学     
可消偏序半群的可消偏序扩张与商序同态
邵海琴, 郭莉琴
天水师范学院 数学与统计学院, 甘肃 天水 741001
The extension on cancellative partial order and quotient ordered homomorphism of cancellative partially ordered semigroup
SHAO Haiqin, GUO Liqin
School of Mathematics and Statistics Institute, Tianshui Normal University, Tianshui 741001, Gansu Province, China
 全文: PDF(929 KB)  
摘要： 引入偏序半群的商半拟序的概念，利用商半拟序给出了可消偏序半群上的偏序可扩张为可消偏序的充分条件.通过偏序半群的半拟序σ、模σ的闭半拟链，商半拟序和偏序扩张以及可消偏序半群的可消偏序扩张，对偏序半群的商序同态进行了刻画，得到了若干重要的结论.
关键词： 可消偏序半群;  半拟序;  商半拟序;  闭半拟链;  偏序扩张;  可消偏序扩张;  商序同态    
Abstract: This paper studies the cancellative partial ordered extension and properties of quotient ordered homomorphisms of cancellative partially ordered semigroups(CPOS). The notion on quotient semi-pseudoorder of partially ordered semigroup(POS) is introduced. With the quotient semi-pseudoorder of CPOS and using the method of partial ordered extension of POS, the sufficient condition for extending a cancellative partial order of CPOS to another cancellative partial order is derived. It is also shown that quotient ordered homomorphism of partially ordered semigroup POS can be depicted by semi-pseudoorder σ, closed semi-pseudochain of modulo σ, quotient semi-pseudoorder, partial ordered extension of partially ordered semigroup, and cancellative partial ordered extension of CPOS. Some important conclusions are obtained.
Key words: cancellative partially ordered semigroup    semi-pseudoorder    quotient semi-pseudoorder    closed semi-pseudochain    partial ordered extension    cancellative partial ordered extension    quotient ordered homomorphism
收稿日期: 2014-10-20 出版日期: 2016-05-01
CLC:  O152.7  
基金资助: 甘肃省教育厅科学研究基金项目（1108B-03）；天水师范学院中青年教师科研资助项目（TSA1311）.
作者简介: 邵海琴(1971-),ORCID:http://orcid.org/0000-0002-2409-9696,女,硕士,副教授,主要从事偏序代数研究,E-mail:shaohq12@163.com.
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引用本文:

邵海琴, 郭莉琴. 可消偏序半群的可消偏序扩张与商序同态[J]. 浙江大学学报（理学版）, 2016, 43(5): 512-516.

SHAO Haiqin, GUO Liqin. The extension on cancellative partial order and quotient ordered homomorphism of cancellative partially ordered semigroup. Journal of Zhejiang University (Science Edition), 2016, 43(5): 512-516.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.002    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I5/512

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