Topological representation of double Boolean algebras

被引：0
作者：
Prosenjit Howlader
Mohua Banerjee
机构：
[1] Indian Institute of Technology Kanpur,Department of Mathematics and Statistics
来源：
Algebra universalis | 2023年 / 84卷
关键词：
Boolean algebra; Double Boolean algebra; Topological representation; Duality; Formal concept; Object oriented concept; 06B15; 06D50; 06E15; 06E75;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The article proves topological representations for some classes of double Boolean algebras (dBas). In particular, representation theorems characterising fully contextual and pure dBas are obtained. Duality results for fully contextual and pure dBas are also established.
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  • [1] Balbiani P(2012)Deciding the word problem in pure double Boolean algebras J. Appl. Logic 10 260-273
  • [2] Breckner BE(2019)A topological representation of double Boolean lattices Stud. Univ. Babeş-Bolyai Math. 64 11-23
  • [3] Săcărea C(1997)Stone duality for lattices Algebra Universalis 37 391-401
  • [4] Hartonas C(1992)A topological representation of lattices Algebra Universalis 29 273-299
  • [5] Dunn JM(2007)Prime ideal theorem for double Boolean algebras Discuss. Math. Gen. Algebra Appl. 27 263-275
  • [6] Hartung G(1970)Representation of distributive lattices by means of ordered Stone spaces Bull. Lond. Math. Soc. 2 186-190
  • [7] Kwuida L(1949)Axiomatic treatment of rank in infinite sets Can. J. Math. 1 337-343
  • [8] Priestley HA(1989)Alexander’s subbase lemma Proc. Am. Math. Soc. 105 262-111
  • [9] Rado R(1936)The theory of representation for Boolean algebras Trans. Am. Math. Soc. 40 37-481
  • [10] Salbany S(1937)Applications of the theory of Boolean rings to general topology Trans. Am. Math. Soc. 41 375-25
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