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A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.

Let H be a subgroup of G. A subset T of elements of G is called a left transversal of H if T contains exactly one element of each left coset of H.

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

The minimum excluded value. The mex of a set S of nonnegative integers is the least nonnegative integer not in the set.

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

A knot having the property that no surgery could possibly yield a counterexample to the Poincaré conjecture is said to satisfy Property P (Adams 1994, p. 262).

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.

In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

For a set S, the span is defined by maxS-minS, where max is the maximum and min is the minimum.