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<div class="csl-entry">Dorfer, G. (1998). <i>Kongruenzen und symmetrische Differenzen auf orthomodularen Verbänden</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-11308</div>
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In this dissertation congruence relations and symmetric differences in orthomodular lattices are studied. After preliminaries in chapter 1 the first two sections of chapter 2 deal with so-called p-ideals, which are exactly the congruence kernels. Amongst other things infimum, supremum, pseudocomplement and relative pseudocomplement in the congruence lattice is explicitly described with p-ideals. In section 2.3 congruence classes are characterized and represented by means of the corresponding p-ideal. From these results congruence regularity, -permutability and -uniformity for orthomodular lattices is derived in 2.4. In chapter 3 we first determine all possibilities to define a symmetric difference in an orthomodular lattice by a term function and then investigate these operations. It turns out that 4 operations out of the 6 that emerged are one-sided regular and one-sided invertible while the other 2 meet regularity or invertibility conditions for Boolean algebras only. Furthermore associativity and distributivity of symmetric differences with respect to meet operations is studied. The main result here is that one of these identities holds if and only if the orthomodular lattice is a Boolean algebra.
en
dc.language
Deutsch
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dc.language.iso
de
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Orthomodularer Verband
de
dc.subject
Kongruenzrelation
de
dc.subject
Symmetrische Differenz
de
dc.title
Kongruenzen und symmetrische Differenzen auf orthomodularen Verbänden
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Gerhard Dorfer
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E104 - Institut für Algebra und Diskrete Mathematik