Weakly Orthomodular and Dually Weakly Orthomodular Lattices
نویسندگان
چکیده
منابع مشابه
Orthomodular Lattices
The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings – as a relationa...
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Sachs (Can J Math 14:451–460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundation...
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If X is a variety of orthomodular lattices generated by a finite orthomodular lattice the MacNeille completion of every algebra in X again belongs to X. AMS subject classilkatioo (1980). 06-xX
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Let L be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the Borceux-Van den Bossche conditions.
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We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lat...
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ژورنال
عنوان ژورنال: Order
سال: 2018
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-017-9448-x