F. Borceux, G. Van den Bossche, "Algebra in a Localic Topos with Applications to Ring Theory"
1983 | pages: 248 | ISBN: 3540127119 | PDF | 8,2 mb
Sheaves of algebras on a topological space appear in man). problems in mathematics and their interest has no longer to be demonstrated. The purpose of this publication is to study the localizations of the category of sheaves of It algebras, where is a finitary algebraic theory, and the extent to which it characterizes the topological base space. The techniques developed to solve these problems, applied to the case of modules on a ring R, provide new results on pure ideals and the representation of rings. As a matter of fact we develop our study in the more general and more natural context of a theory ~ internally defined with respect to a topos of sheaves on a frame (i.e. a complete Heyting algebra; for example the algebra of open subsets of a topological space).
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