偏序集到完全分配格的并稠嵌入
Join Dense Embeddings of Posets in Completely Distributive Lattices
DOI: 10.12677/PM.2015.54024, PDF, HTML, XML, 下载: 2,354  浏览: 7,571  国家自然科学基金支持
作者: 徐晓泉:南昌师范学院数学与计算机系,江西 南昌
关键词: 偏序集子集系统完全分配格并稠嵌入正则关系Poset Subset System Completely Distributive Lattice Join Dense Embedding Regular Relation
摘要: 基于正则关系,建立了偏序集到完全分配格的并稠嵌入定理,证明了在同构的意义下,偏序集到完全分配格的并稠嵌入是唯一的,即均是由一些正则关系诱导的并稠嵌入。
Abstract: Based on regular relations, the join dense embedding theorem of posets in completely distributive lattices is established, and it is proved that up to isomorphism, such embeddings are unique, that is, they all are the join dense embeddings induced by certain regular relations on posets.
文章引用:徐晓泉. 偏序集到完全分配格的并稠嵌入[J]. 理论数学, 2015, 5(4): 156-166. http://dx.doi.org/10.12677/PM.2015.54024

参考文献

[1] Raney, G.N. (1953) A subdirect-union representation for completely distributive complete lattices. Proceedings of the American Mathematical Society, 4, 518-522.
http://dx.doi.org/10.1090/s0002-9939-1953-0058568-4
[2] Raney, G.N. (1960) Tight Galois connections and complete distributivity. Transactions of the American Mathematical Society, 97, 418-426.
http://dx.doi.org/10.1090/S0002-9947-1960-0120171-3
[3] Bruns, G. (1961) Distributivität und subdirekte Zerlegbarkeit vollständiger Vergände. Archiv der Mathematik, 12, 418- 426.
[4] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M. and Scott, D.S. (1980) A compendium of continuous lattices. Springer Verlag.
http://dx.doi.org/10.1007/978-3-642-67678-9
[5] Lawson, J.D. (1969) Topological semilattices with small semilattices. Journal London Mathematical Society, 2, 719- 724.
http://dx.doi.org/10.1112/jlms/s2-1.1.719
[6] Bandelt, H.J. and Erné, M. (1984) Representations and embeddings of M-distributive lattices. Houston Journal of Mathematics, 10, 315-324.
[7] Xu, X.Q. (1995) Construction of homomorphisms of M-continuous lattices. Transactions of the American Mathematical Society, 347, 3167-3175.
[8] 徐晓泉 (1995) M-连续格到Hilbert方体的嵌入. 数学学报, 38, 827-830.
[9] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M. and Scott, D.S. (2003) Continuous lattices and domains. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511542725
[10] Xu, X.Q. (1995) Embeddings of Zdomains in cubes. In: Fuzzy Logic and its Applications, Kluwer Academic Publishers, The Netherlands, 333-342.
http://dx.doi.org/10.1007/978-94-009-0125-4_33
[11] Zareckiǐ, K.A. (1963) The semigroup of binary relations. Matematicheskii Sbornik, 61, 291-305.
[12] Markowsky, G. (1972) Idempotents and product representations with ap-plications to the semigroup of binary relations. Semigroup Forum, 5, 95-119.
http://dx.doi.org/10.1007/bf02572880
[13] Schein, B.M. (1976) Regular elements of the semigroup of all binary relations. Semigroup Forum, 13, 95-102.
http://dx.doi.org/10.1007/BF02194925
[14] Bandelt, H.J. (1980) Regularity and complete distributivity. Semigroup Forum, 19, 123-126.
http://dx.doi.org/10.1007/BF02572509
[15] Bandelt, H.J. (1982) On regularity classes of binary relations. In: Universal Algebra and Applications, Banach Center Publications, Vol. 9, PWN Polish Scientific Publishers, Warsaw, 329-333.
[16] Yang, J.C. (1969) A theorem on the semigroup of binary relations. Proceedings of the American Ma-thematical Society, 22, 134-135.
http://dx.doi.org/10.1090/S0002-9939-1969-0241557-6
[17] Xu, X.Q. and Liu Y.M. (2003) Relational representations of hypercontinuous lattices. In: Domain Theory, Logic, and Computation, Kluwer Academic Publishers, 65-74.
http://dx.doi.org/10.1007/978-94-017-1291-0_3
[18] Xu, X.Q. and Liu Y.M. (2004) Regular relations and strictly completely regular ordered spaces. Topology and Its Applications, 135, 1-12.
http://dx.doi.org/10.1016/S0166-8641(03)00108-1
[19] Xu, X.Q. and Liu Y.M. (2004) Regular relations and monotone normal ordered spaces. Chinese Ann. of Math., 25B, 157-164.
http://dx.doi.org/10.1142/S0252959904000160
[20] Xu, X.Q. and Luo M.K. (2006) Regular relations and nor-mality of topologies. Semigroup Forum, 72, 477-480.
http://dx.doi.org/10.1007/s00233-004-0179-0
[21] 徐晓泉, 刘应明 (2008) 正则关系与完全正则空间. 数学年刊, 29A, 819-828.
[22] 徐晓泉, 罗懋康 (2009) 正则关系与正规空间. 数学学报, 52, 393-402.
[23] Baranga, A. (1996) Z-continuous posets. Discrete Mathematics, 152, 33-45.
http://dx.doi.org/10.1016/0012-365X(94)00307-5