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A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a meet-homomorphism, then h is a meet-embedding.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and onto, then it is a meet-isomorphism provided that it preserves meets.

In French and German usage, one milliard equals 10^9=1000000000. American usage does not have a number called the milliard, instead using the term billion to denote 10^9. ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

A class of automata similar to cellular automata but which have a single "active" cell instead of updating all cells in parallel. In a mobile automaton, the evolution rules ...