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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (5): 521-525    DOI: 10.3785/j.issn.1008-9497.2019.05.001
数学与计算机科学     
弱拉回平坦序S-系对序幺半群的刻画
梁星亮, 龙斌, 徐盼盼
陕西科技大学 文理学院，陕西 西安 710021
Characterizarion of pomonoids by weakly pullback flat S-posets
LIANG Xingliang, LONG Bin, XU Panpan
School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China
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摘要： 设S是序幺半群，借助环模理论以及半群S-系理论方法，在序S-系范畴中研究了弱拉回平坦性质。刻画了弱拉回平坦序S-系关于直积封闭的序幺半群类以及弱拉回平坦性质与其他性质一致的序幺半群类，讨论了循环序S-系具有拉回平坦覆盖的条件，进而推广了S-系的一些重要结果。
关键词： 序S-系;  S-系;  序幺半群;  幺半群;  直积;  覆盖    
Abstract: Let S be a pomonoid. By using the theory of modules over rings and the theory of S-acts over semigroups, the weakly pullback flat S-posets in the category of S-posets are investigated. Pomonoids over which weakly pullback flatness of S-posets are preserved under direct products, and pomonoids over which weakly pullback flatness coincides with other flatness for S-posets are characterized. Moreover, some conditions that a cyclic S-poset has a weakly pullback flat cover are discussed, and some important results on weakly pullback flat right S-acts are extended.LIANG Xingliang, LONG Bin, XU Panpan（School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China）Characterizarion of pomonoids by weakly pullback flat S-posets.
Key words: S-poset    S-act    pomonoid    monoid    direct product    cover
收稿日期: 2018-04-16 出版日期: 2019-09-25
CLC:  O152.7  
基金资助: 陕西省自然科学基础研究计划项目(2017JQ1026)；陕西省教育厅自然科学研究项目(17JK0102).
作者简介: 梁星亮(1987—)，ORCID：http://orcid.org/0000- 0002-4517-8684 ，男，博士，讲师， 主要从事半群代数理论研究，E-mail:lxl_119@126.com.
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引用本文:

梁星亮, 龙斌, 徐盼盼. 弱拉回平坦序S-系对序幺半群的刻画[J]. 浙江大学学报（理学版）, 2019, 46(5): 521-525.

LIANG Xingliang, LONG Bin, XU Panpan. Characterizarion of pomonoids by weakly pullback flat S-posets. Journal of Zhejiang University (Science Edition), 2019, 46(5): 521-525.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.05.001    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I5/521

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