منابع مشابه
Closure lattices
Closure spaces have been previously investigated by Paul Edelman and Robert Jami-son as \convex geometries". Consequently, a number of the results given here duplicate theirs. However, we employ a slightly diierent, but equivalent, deening axiom which gives a new avor to our presentation. The major contribution is the deenition of a partial order on all subsets, not just closed (or convex) subs...
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The concept of a closure operator ∇ in an ADL R was introduced. If ∇R is the set of all ∇−invariant elements of R, then the concepts of ∇R−ideal, ∇R−prime ideal are introduced. The interrelations between ∇R−prime ideal and minimal prime ideal of R are derived. If B is the Birkhoff centre of R, then a sufficient condition is derived for a B−ideal to be a minimal prime ideal of R. Mathematics Sub...
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Article history: Received 15 January 2015 Received in revised form 4 June 2015 Accepted 26 July 2015 Available online 7 August 2015
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Closure operators are abundant in mathematics; here are a few examples. Given an algebraic structure, such as group, ring, field, lattice, vector space, etc., taking the substructure generated by a set, i.e., the least substructure which includes that set, is a closure operator. Given a binary relation, taking the relation with certain properties, such as reflexive, transitive, equivalence, etc...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1941
ISSN: 0386-2194
DOI: 10.3792/pia/1195578911