منابع مشابه
A Proof of Weinberg’s Conjecture on Lattice-ordered Matrix Algebras
Let F be a subfield of the field of real numbers and let Fn (n ≥ 2) be the n× n matrix algebra over F. It is shown that if Fn is a lattice-ordered algebra over F in which the identity matrix 1 is positive, then Fn is isomorphic to the lattice-ordered algebra Fn with the usual lattice order. In particular, Weinberg’s conjecture is true. Let L be a totally ordered field, and let Ln (n ≥ 2) be the...
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We consider varieties of pointed lattice-ordered algebras satisfying a restricted distributivity condition and admitting a very weak implication. Examples of these varieties are ubiquitous in algebraic logic: integral or distributive residuated lattices; their {·}-free subreducts; their expansions (hence, in particular, Boolean algebras with operators and modal algebras); and varieties arising ...
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The notion of Wiener-Hopf type factorization is introduced in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups. Factorizations of 2 x 2 block triangular matrix functions with elementary functions on the main diagonal are studied in detail. A conjectl,lre is formulated concerning characterization of dual groups with the property that every ...
متن کاملRoughness in Lattice Ordered Effect Algebras
Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ord...
متن کاملFinite homogeneous and lattice ordered effect algebras
Effect algebras (or D-posets) have recently been introduced by Foulis and Bennett in [1] for study of foundations of quantum mechanics. (See also [2], [3].) The prototype effect algebra is (E(H),⊕, 0, I), where H is a Hilbert space and E(H) consists of all self-adjoint operators A of H such that 0 ≤ A ≤ I. For A,B ∈ E(H), A⊕B is defined iff A+B ≤ 1 and then A⊕B = A+B. E(H) plays an important ro...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.02.028