Sheaves over Boolean spaces. (English) Zbl 1282.06015
Hemakul, Wanida (ed.) et al., Proceedings of the international conference on algebra 2010: advances in algebraic structures, Yogjakarta, Indonesia, October 7–10, 2010. Dedicated to Shum Kar-Ping on the occasion of his 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4366-30-4/hbk; 978-981-4366-31-1/ebook). 631-643 (2012).
In this invited talk, the author gives a couple of generalisations of facts known for Boolean algebras. At first, he develops a generalisation of Stone duality between Boolean algebras and Boolean spaces to a duality between almost Boolean algebras and sheaves of sets over Boolean spaces. Next, he gives the definition of almost Boolean rings and shows a duality between these structures and almost Boolean algebras. Finally, he presents a number of structures that generalise almost Boolean algebras and discusses their properties, among them almost distributive lattices (ADLs), pseudo-complemented almost distributive lattices and Stone ADLs. The paper gives essentially a survey of part of the author’s research of the last three and a half decades; see, e.g. [Zbl 0311.06008; Zbl 0473.06008; Zbl 0982.06011; Zbl 1059.06009].
For the entire collection see [Zbl 1245.00043].
For the entire collection see [Zbl 1245.00043].
Reviewer: Klaus D. Kiermeier (Berlin)
MSC:
06E75 | Generalizations of Boolean algebras |
06D50 | Lattices and duality |
06D75 | Other generalizations of distributive lattices |
06E15 | Stone spaces (Boolean spaces) and related structures |
54H10 | Topological representations of algebraic systems |