In Abstract Algebra
The relation of divisibility turns the set of non-negative integers into a partially ordered set, in fact into a complete distributive lattice. The largest element of this lattice is 0 and the smallest is 1. The meet operation ^ is given by the greatest common divisor and the join operation v by the least common multiple. This lattice is isomorphic to the dual of the lattice of subgroups of the infinite cyclic group .
Read more about this topic: Divisor
Famous quotes containing the words abstract and/or algebra:
“All abstract sciences are nothing but the study of relations between signs.”
—Denis Diderot (1713–1784)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)