Orthomodular Lattices Which Can Be Covered by Finitel Y Many Blocks
نویسنده
چکیده
In our paper [3] we considered four finiteness conditions for an orthomodular lattice (abbreviated: OML) L and conjectured their equivalence. The only question left open in that paper was whether an OML L which can be covered by finitely many blocks (maximal Boolean subalgebras) has only finitely many blocks. In this paper we give an affirmative answer to this question , in fact , we prove the slightly stronger result:
منابع مشابه
Epimorphisms in Certain Varieties of Algebras
We prove a lemma which, under restrictive conditions, shows that epimorphisms in V are surjective if this is true for epimorphisms from irreducible members of V . This lemma is applied to varieties of orthomodular lattices which are generated by orthomodular lattices of bounded height, and to varieties of orthomodular lattices which are generated by orthomodular lattices which are the horizonta...
متن کاملOrthomodular Lattices with Rich State Spaces Orthomodular Lattices with Rich State Spaces
We introduce a new construction technique for orthomodular lattices. In contrast to the preceding constructions, it admits rich spaces of states (=probability measures), i.e., for each pair of incomparable elements a; c there is a state s such that s(a) = 1 > s(c). This allowed a progress in many questions that were open for a long time; among others we prove that there is a continuum of variet...
متن کاملOrthomodular lattices with fully nontrivial commutators
An orthomodular lattice L is said to have fully nontrivial commutator if the commutator of any pair x, y ∈ L is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbert...
متن کاملAmalgamation of Ortholattices
We show that the variety of ortholattices has the strong amalgamation property and that the variety of orthomodular lattices has the strong Boolean amalgamation property, i.e. that two orthomodular lattices can be strongly amalgamated over a common Boolean subalgebra. We give examples to show that the variety orthomodular lattices does not have the amalgamation property and that the variety of ...
متن کاملOrthomodular Lattices with Rich State Spaces
We introduce a new construction technique for orthomodular lattices. In contrast to the preceding constructions, it admits rich spaces of states (=probability measures), i.e., for each pair of incomparable elements a; c there is a state s such that s(a) = 1 > s(c). This allowed a progress in many questions that were open for a long time; among others we prove that there is a continuum of variet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007