Abstract
Some properties of projective stone algebras are exhibited, which are connected with the ordered set of prime ideals. From this we derive a simple characterization of finite projective Stone algebras, and of those projective Stone algebras, whose centre is a projective Boolean algebra, and whose dense set is a projective Stone algebras, whose centre is a projective Boolean algebra, and whose dense set is a projective distributive lattice. Finally, we give some conditions under which a Stone algebra has no chains of type λ, where λ is an infinite regular cardinal.
The results of this paper are part of the author's Ph.D. Thesis written under the direction of S. Koppelberg. The author wishes to express his gratitude to Prof. Koppelberg for her guidance and her patience.
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Düntsch, I. Projectivity, prime ideals, and chain conditions of Stone algebras. Algebra Universalis 14, 167–180 (1982). https://doi.org/10.1007/BF02483918
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DOI: https://doi.org/10.1007/BF02483918