S-Poset内射包的一个注记
A Note on Injective Hulls of S-Poset
DOI: 10.12677/PM.2021.111008, PDF,   
作者: 李玉林：长安大学理学院，陕西 西安
关键词: 序半群；S-Poset；内射包；Posemigroup； S-Poset； Injective Hull
摘要: 设S是一个序半群，本文采用序代数理论和quantale理论中的研究方法，在以S-poset为对象以S-次可乘映射为态射的范畴中，对于一类特殊的态射ε≤，构造了S-poset的内射包。本文的结果不仅推广了基于S是序幺半群时的相应结果，而且也得到了剩余S-poset的内射包。
Abstract: Let S be a posemigroup. Inspired by the study method of order algebra theory and quantale theory, we construct an  -injective hull for an arbitrary S-poset in the category of S-poset with S-submultiplicative morphisms with respect to a specific class of morphisms ε≤. The results of the present paper not only generalize the corresponding results based on S be a pomonoid but also lead to injective hull for residuated S-poset.
文章引用：李玉林. S-Poset内射包的一个注记[J]. 理论数学, 2021, 11(1): 47-52. https://doi.org/10.12677/PM.2021.111008

参考文献

[1] Skornyakov, L.A. (1986) Injectivity of All Ordered Left Polygons over a Monoid. Vestnik Moskovskogo Universiteta, Seriya I, 3, 17-19.
[2] Kilp, M., Knauer, U. and Mikhalev, A.V. (2000) Monoids, Acts and Categories (With Appli-cations to Wreath Products and Graphs). Walter de Gruyter, Berlin, New York. [Google Scholar] [CrossRef] 
[3] 王蕊, 赵彬. Quantale代数及其代数理想[J]. 模糊系统与数学, 2010, 24(2): 44-49.
[4] 李伟. S-代数的表示范畴[J]. 西南大学学报(自然科学版), 2010, 32(4): 101-104.
[5] Fakhruddin, S.M. (1998) On the Category of S-Posets. Acta Mathematica Scientia, 52, 85-92.
[6] Zhang, X. and Laan, V. (2007) On Homological Classification of Pomonoids by Regular Weak Injectivity Properties of S-Posets. Central European Journal of Mathematics, 5, 181-200. [Google Scholar] [CrossRef] 
[7] Ebrahimi, M.M., Mahmoudi, M. and Rasouli, H. (2010) Banaschewski’s Theorem for S-Posets: Regular Injectivity and Completeness. Semigroup Forum, 80, 313-324. [Google Scholar] [CrossRef] 
[8] 张霞, 徐彦涛. 偏序群S上S-偏序系的内射包[J]. 华南师范大学学报(自然科学版), 2014, 46(4): 12-15.
[9] 武全, 赵彬. 模糊S-偏序集的内射壳[J]. 吉林大学学报(理学版), 2017, 55(2): 216-224.
[10] 毛徐新, 徐罗山. S-超连续偏序集的性质及等价刻画[J]. 计算机工程与应用, 2015, 51(1): 9-12.
[11] Zhang, X. and Laan, V. (2015) On Injective Hulls of S-Posets. Semigroup Forum, 91, 62-70. [Google Scholar] [CrossRef] 
[12] Davey, B.A. and Priestley, H.A. (2002) Introduction to Lattices and Order. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 
[13] 谢祥云. 序半群引论[M]. 北京: 科学出版社, 2001.
[14] Adámek, J., Herrlich, H. and Strecker, G.E. (1990) Abstract and Concrete Categories: The Joy of Cats. Wiley, New York.

为你推荐