Archimedean, semiperfect and $\pi $-regular lattice-ordered algebras with polynomial constraints are $f$-algebras
نویسندگان
چکیده
منابع مشابه
Finite 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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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...
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Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0712623-0