Closure operators and Galois theory in lattices
نویسندگان
چکیده
منابع مشابه
Closure Operators in Almost Distributive Lattices
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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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: Transactions of the American Mathematical Society
سال: 1944
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1944-0010556-9