Finite homogeneous and lattice ordered effect algebras
نویسنده
چکیده
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 role in the foundations of quantum mechanics [4], [5].
منابع مشابه
A classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کاملAutomata theory based on unsharp quantum logic
By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and on...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
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 کاملGeneralizations of Boolean products for lattice-ordered algebras
It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 272 شماره
صفحات -
تاریخ انتشار 2003