The block structure of complete lattice ordered effect algebras
نویسندگان
چکیده
منابع مشابه
the structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولRoughness 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...
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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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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 ...
متن کاملLattice effect algebras densely embeddable into complete ones
An effect algebraic partial binary operation ⊕ defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion b E of E there exists an effect algebraic partial binary operation b ⊕ then b ⊕ need not be an extension of ⊕. Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2007
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700036867