Conditional associativity in orthomodular lattices
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Jeannine J. M. Gabriëls
Abstract
For orthomodular lattices the word problem is still not decided, an important obstacle is the lack of distributivity. But also the absence of the associativity law for operations other than the lattice operations meet and join causes difficulties. In this paper we treat some aspects of associativity in orthomodular lattices.
There are six out of 96 orthomodular operations which are associative. We search for orthomodular lattice operations which fulfil the associative identity under some conditions. Specifically we assume that some arguments commute and identify, for each operation, sufficient conditions under which a triple of elements fulfils the respective associativity identity.
The author was supported by the Czech Ministry of Education under project RVO13000.
Acknowledgement
The author thanks the anonymous reviewers for careful proofreading.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras
