245 research outputs found
Two-valued states on Baer -semigroups
In this paper we develop an algebraic framework that allows us to extend
families of two-valued states on orthomodular lattices to Baer -semigroups.
We apply this general approach to study the full class of two-valued states and
the subclass of Jauch-Piron two-valued states on Baer -semigroups.Comment: Reports on mathematical physics (accepted 2013
Linear representations of regular rings and complemented modular lattices with involution
Faithful representations of regular -rings and modular complemented
lattices with involution within orthosymmetric sesquilinear spaces are studied
within the framework of Universal Algebra. In particular, the correspondence
between classes of spaces and classes of representables is analyzed; for a
class of spaces which is closed under ultraproducts and non-degenerate finite
dimensional subspaces, the latter are shown to be closed under complemented
[regular] subalgebras, homomorphic images, and ultraproducts and being
generated by those members which are associated with finite dimensional spaces.
Under natural restrictions, this is refined to a --correspondence between
the two types of classes
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