Reflections and coreflections in generalized orthomodular lattices
Regular elements in complete uniquely complemented lattices
Relations between some dimensions of semimodular lattices
The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiński and Puczyłowski.
Relative Complements in the Weak Congruence Lattice
Relative conditional expectations on a logic
In this paper, the authors introduce the notion of conditional expectation of an observable on a logic with respect to a sublogic, in a state , relative to an element of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.
Relative Pseudo-Complements, Join-Extensions, and Meet-Retractions.
Relatively additive states on quantum logics
In this paper we carry on the investigation of partially additive states on quantum logics (see [2], [5], [7], [8], [11], [12], [15], [18], etc.). We study a variant of weak states — the states which are additive with respect to a given Boolean subalgebra. In the first result we show that there are many quantum logics which do not possess any 2-additive central states (any logic possesses an abundance of 1-additive central state — see [12]). In the second result we construct a finite 3-homogeneous...
Relatively complemented ordered sets
We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.
Remarks about measures on orthomodular posets
Remarks on Ideals in Join-Semilattices.
Remarque sur les treillis complets pseudo complémentes
Representation of algebraic distributive lattices with ℵ1 compact elements as ideal lattices of regular rings.
We prove the following result: Theorem. Every algebraic distributive lattice D with at most ℵ1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R.(By earlier results of the author, the ℵ1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. Furthermore, if the largest element of D is compact, then one can assume that R is unital, respectively,...
Representations of finite lattices by orders on finite sets
Representations of Topological Semigroups
Residuation Theory (Book Review by R. McFadden.
Riduzioni omotopicamente invarianti di insiemi parzialmente ordinati
Ring-like structures corresponding to generalized orthomodular lattices
Ring-like structures derived from -lattices with antitone involutions
Using the concept of the -lattice introduced recently by V. Snášel we define -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.