兰州大学机构库 >数学与统计学院
关于(序) S-系平坦性质的若干研究
Alternative TitleSome studies on the flatness of S-acts (S-posets)
梁星亮
Thesis Advisor罗彦锋
2016-06-03
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword纯性满同态 GP-序平坦性 平坦性质 弱挠自由性 同调分类问题 条件(PF') 条件GP-(P) (序) S-系 (序)幺半群
Abstract通过研究(序) S-系的平坦性质, 来刻画(序)幺半群的结构特征。首先,在S-系范畴中引入了条件(PF')和条件GP-(P),利用这两个新性质刻画了一些重要的幺半群的类,诸如:右可消幺半群、广义正则幺半群、群等。其次,研究了序S-系范畴中满同态的纯性问题。通过引入一些具有某些纯性条件的满同态,给出了序S-系中平坦性质的等价刻画。特别地, 我们给出了一种证明有向上极限保持序S-系平坦性质的新方法。最后,研究了序S-系的GP-序平坦性和弱挠自由性,进一步考虑了与它们有关的同调分类问题。
Other AbstractThe S-act (S-poset) theory of (ordered) semigroups as an important branch of the (ordered) semigroup theory, it plays an important role not only in studying properties of (ordered) semigroups but also in other mathematical areas, such as graph theory and algebraic automata theory. In this thesis, we characterize (po-)monoids by using flatness properties of S-acts (S-posets) over (po-)monoids. This thesis contains six chapters.In Chapter 1, we introduce the research background about the theory of S-acts (S-posets), and then list the main results of this thesis. Finally, we introduce some basic definitions and facts that are exactly what we need in this thesis.In Chapter 2, we study S-acts satisfying Condition (PF'). First, we introduce Condition (PF') in the category of S-acts, and discuss relations between this property and weak pullback flatness (resp., Condition (P')). Moreover. we prove that Condition (PF') coincides exactly with the conjunction of Conditions (P') and (E'). Second, we give some characterizations of monoids by Condition (P'') of (cyclic, Rees factor) acts. Particularly, we characterize monoids under which Condition (PF') coincides with Condition (P') (resp., weak pullback flatness, strong flatness) for Rees factor acts. Finally, we investigate Conditions (P'), (E') and (PF') using the purity of epimorphisms. In Chapter 3, we study S-acts satisfying Condition GP-(P). Corresponding to GP-flatness in the category of S-acts, we first define Condition GP-(P), which is a generalization of Condition (PWP). Moreover, we study the homological classification problems of monoids by using Condition GP-(P) of their (cyclic, Rees factor) acts. Especially, the classes of some important monoids are characterized, such as right cancellative monoids, generally regular monoids, groups and so on. And then the correlative conclusions about Condition (PWP) are generalized. Second, we present some equivalent characterizations of monoids (such as cancellative monoids, left groups, etc.) by investigating their diagonal acts satisfying Condition GP-(P). Finally, using quasi G-2-pure epimorphisms and quasi-2-pure epimorphisms, we obtain some new equivalent descriptions of Condition GP-(P) (resp., Condition (PWP)).In Chapter 4, we research on purity conditions of epimorphisms in the category of S-posets. First, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness propert...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225373
Collection数学与统计学院
Recommended Citation
GB/T 7714
梁星亮. 关于(序) S-系平坦性质的若干研究[D]. 兰州. 兰州大学,2016.
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