scholarly journals The space of Stone representation and constructions of extensions

2008 ◽  
pp. 169-172
Author(s):  
A.G. Chentsov ◽  
Keyword(s):  
Stone Representation

Pure Compactifications in Quasi-Primal Varieties

1976 ◽  
Vol 28 (1) ◽  
pp. 50-62 ◽  
Author(s):  
Walter Taylor
Keyword(s):  
General Theory ◽  
Representation Theorem ◽  
Boolean Algebras ◽  
Finite Algebras ◽  
Stone Representation

We prove that is quasi-primal, then every algebra in HSPhas a pure embedding into a product of finite algebras. For a general theory of varieties for which every can be purely embedded in an equationally compact algebra , and for all notions not explained here, the reader is referred to [38; 6; or 5]. This theorem was known for Boolean algebras simply as a corollary of the Stone representation theorem and the fact that in the variety of Boolean algebras, all embeddings are pure [2].

scholarly journals Ideal completion and Stone representation of ideal-distributive ordered sets

1992 ◽  
Vol 44 (1-3) ◽  
pp. 95-113 ◽  
Author(s):  
Elias David ◽  
Marcel Erné
Keyword(s):  
Ordered Sets ◽  
Ideal Completion ◽  
Stone Representation

The Stone representation of an atomic complete Boolean algebra is Marczewski–Burstin representable

2012 ◽  
Vol 18 (2) ◽  
Author(s):  
Artur Bartoszewicz ◽  
Andrzej Kowalski
Keyword(s):  
Boolean Algebra ◽  
Complete Boolean Algebra ◽  
Stone Representation

Stone representation theorem for Boolean algebras in the topos MSet

2021 ◽  
pp. 1-10
Author(s):  
Mojgan Mahmoudi ◽  
Sara Sepahani
Keyword(s):  
Representation Theorem ◽  
Boolean Algebras ◽  
Stone Representation

scholarly journals On Fuzzy Ideals ofBL-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Biao Long Meng ◽  
Xiao Long Xin
Keyword(s):  
Prime Ideal ◽  
Distributive Lattice ◽  
Fuzzy Set ◽  
Representation Theorem ◽  
Prime Ideals ◽  
Converse Implication ◽  
Fuzzy Ideal ◽  
Stone Representation

In this paper we investigate further properties of fuzzy ideals of aBL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of aBL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime idealωis a fuzzy irreducible ideal if and only ifω0=1and|Im⁡(ω)|=2. We give the Krull-Stone representation theorem of fuzzy ideals inBL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of aBL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.

scholarly journals An extension of the Stone representation for orthomodular lattices

1973 ◽  
Vol 27 (1) ◽  
pp. 21-30 ◽  
Author(s):  
W. H. Graves ◽  
S. A. Selesnick
Keyword(s):  
Orthomodular Lattices ◽  
Stone Representation

scholarly journals A noncommutative theory of Bade functionals

1991 ◽  
Vol 33 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Don Hadwin ◽  
Mehmet Orhon
Keyword(s):  
Banach Space ◽  
Linear Functional ◽  
Hausdorff Space ◽  
Boolean Algebras ◽  
Representation Space ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Banach Modules ◽  
Key Concepts ◽  
Stone Representation

Since the pioneering work of W. G. Bade [3, 4] a great deal of work has been done on bounded Boolean algebras of projections on a Banach space ([11, XVII.3.XVIII.3], [21, V.3], [16], [6], [12], [13], [14], ]17], [18], [23], [24]). Via the Stone representation space of the Boolean algebra, the theory can be studied through Banach modules over C(K), where K is a compact Hausdorff space. One of the key concepts in the theory is the notion of Bade functionals. If X is a Banach C(K)-module and x ε X, then a Bade functional of x with respect to C(K) is a continuous linear functional α on X such that, for each a in C(K) with a ≥ 0, we have(i) α (ax) ≥0,(ii) if α (ax) = 0, then ax = 0.

A Simple Proof of the Daniell-Stone Representation Theorem

1983 ◽  
Vol 90 (6) ◽  
pp. 396-397
Author(s):  
Jürgen Kindler
Keyword(s):  
Simple Proof ◽  
Representation Theorem ◽  
Stone Representation

scholarly journals Gelfand theorem implies Stone representation theorem of Boolean rings

1995 ◽  
Vol 18 (4) ◽  
pp. 701-704
Author(s):  
Parfeny P. Saworotnow
Keyword(s):  
Boolean Algebra ◽  
Topological Space ◽  
Representation Theorem ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Boolean Rings ◽  
Stone Representation ◽  
Stone Theorem

Stone Theorem about representing a Boolean algebra in terms of open-closed subsets of a topological space is a consequence of the Gelfand Theorem about representing aB∗- algebra as the algebra of continuous functions on a compact Hausdorff space.

scholarly journals Representation of Boolean hypolattices

1981 ◽  
Vol 24 (3) ◽  
pp. 389-404 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Representation Theorem ◽  
Boolean Lattice ◽  
Principal Result ◽  
Direct Sum ◽  
Boolean Lattices ◽  
Stone Representation ◽  
Relative Convexity ◽  
Small Product

The principal result is a representation theorem for relatively-distributive, relatively complemented hypolattices with zero, generalizing the Stone representation theorem for a Boolean lattice. It uses the small product of a family of Boolean lattices which are maximal sublattices of the hypolattice. The paper also characterizes the maximal sublattices when the hypolattice is coherent; and it gives several examples of hypolattices, including hypolattices of subgroups and of ideals by direct sum, and examples from relative convexity, relative closure, and cofinality.

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