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THE INTERNAL IDEAL LATTICE IN THE TOPOS OF M-SETS | ||
Journal of Sciences, Islamic Republic of Iran | ||
مقاله 5، دوره 5، شماره 2، آذر 1994 اصل مقاله (363.29 K) | ||
چکیده | ||
We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the category of lattices. In this paper, we construct the (internal) ideal lattice T(A) of a lattice A in the topos of M-sets for a monoid M. The process of the construction of Y(A) is so that it can also be done in any arbitrary topos whose ingredients are known. Finally, we consider the lattice structure of T(A) for some special kind of lattices A in the topos of M-sets and show, among other things, that if A is an internally complete M-Boolean algebra then Y(A) is an M-Stone lattice | ||
عنوان مقاله [English] | ||
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چکیده [English] | ||
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آمار تعداد مشاهده مقاله: 1,018 تعداد دریافت فایل اصل مقاله: 1,067 |