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A new proof of the construction theorem for Stone algebras

Author: Tibor Katriňák
Journal: Proc. Amer. Math. Soc. 40 (1973), 75-78
MSC: Primary 06A35
MathSciNet review: 0316335
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Abstract: A simple proof is given of Chen's and Grätzer's theorem, which gives a method to construct a Stone algebra from a Boolean algebra and a distributive lattice with 1 by certain connective conditions between the two given lattices.

References [Enhancements On Off] (What's this?)

  • [1] C. C. Chen and G. Grätzer, Stone lattices. I: Construction theorems, Canad. J. Math. 21 (1969), 884-894. MR 39 #4065a. MR 0242737 (39:4065a)
  • [2] G. Grätzer, Lattice theory. First concepts and distributive lattices, Freeman, San Francisco, Calif., 1971. MR 0321817 (48:184)
  • [3] T. Katriňák, Die Kennzeichnung der distributiven pseudokomplementären Halbverbände, J. Reine Angew. Math. 241 (1970), 160-179. MR 41 #5253. MR 0260629 (41:5253)
  • [4] -, Über eine Konstruktion der distributiven pseudokomplementären Verbände, Math. Nachr. 53 (1972), 85-99. MR 0316334 (47:4882)

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Keywords: Distributive lattice with pseudocomplementation, $ p$-algebra, Stone algebra, Stone lattice, Boolean algebra, pseudocomplement, dense element, closed element
Article copyright: © Copyright 1973 American Mathematical Society

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