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Teorias proposicionales asociadas a estructuras algebraicas (Spanish text)

Posted on:2004-01-31Degree:M.SType:Thesis
University:University of Puerto Rico, Mayaguez (Puerto Rico)Candidate:Morales Irizarry, VirgilioFull Text:PDF
GTID:2465390011466904Subject:Mathematics
Abstract/Summary:
In this thesis, the propositional theories T (μ)(Δ) associated with an algebraic structure Δ such that: groups, rings, modules and lattices are defined. In particular it is proven that there is a one to one correspondence between the algebraic substructures of Δ and models of the propositional theory T(Δ). This definition is also extended for a universal algebra U . In particular, the existence of a one to one correspondence between the congruence relations of the algebra U and models of the propositional theory T U associated with an algebra U is proved. Various examples are presented in detail. Some of these examples are: the integer Z,i=l
    ′′
Z, j=l
    m
i=l
    ′′
Zmi and R2 . Atoms and atom models of the theories T(μ) (Δ) for these examples are also studied. In general, this gives an alternate way to study algebraic structures using these propositional theories and mathematical logic.
Keywords/Search Tags:Algebraic, Propositional, Theories, /italic
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