Displaying similar documents to “Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras”

Lattice effect algebras densely embeddable into complete ones

Zdena Riečanová (2011)

Kybernetika

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An effect algebraic partial binary operation ø p l u s defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion E ^ of E there exists an effect algebraic partial binary operation ⊕ ^ then ⊕ ^ need not be an extension of ⊕ . Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that ⊕ ^ existing on E ^ is an extension of ⊕ defined on E . Further we show that such ⊕ ^ extending ⊕ exists...

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

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A concrete category 𝕂 is (algebraically) if any category of algebras has a full embedding into 𝕂 , and 𝕂 is if there is a class 𝒞 of 𝕂 -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of 0 -lattices which are almost universal.

Decomposition of ℓ -group-valued measures

Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)

Czechoslovak Mathematical Journal

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We deal with decomposition theorems for modular measures μ : L → G defined on a D-lattice with values in a Dedekind complete ℓ -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete ℓ -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition...

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...