| Mathematics and Computer Science |
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| 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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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.
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Received: 16 April 2018
Published: 25 September 2019
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弱拉回平坦序S-系对序幺半群的刻画
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
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