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The characteristic exponent of a field is 1 if the field characteristic is 0 and p if the field characteristic is p.

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

The field of rationals is the set of rational numbers, which form a field. This field is commonly denoted Q (doublestruck Q).

The field of reals is the set of real numbers, which form a field. This field is commonly denoted R (doublestruck R).

The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...

A number x is said to have "n figures" if it takes n digits to express it. The number of figures is therefore equal to one more than the power of 10 in the scientific ...

A ring equipped with a filtration.

A filtration of ideals of a commutative unit ring R is a sequence of ideals ... subset= I_2 subset= I_1 subset= I_0=R, such that I_iI_j subset= I_(i+j) for all indices i,j. ...

A map psi:M->M, where M is a manifold, is a finite-to-one factor of a map Psi:X->X if there exists a continuous surjective map pi:X->M such that psi degreespi=pi degreesPsi ...

A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...