On the scarcity of lattice-ordered matrix algebras II
نویسندگان
چکیده
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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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.
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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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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05171-0