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Let K be an algebraically closed field and let I be an ideal in K(x), where x=(x_1,x_2,...,x_n) is a finite set of indeterminates. Let p in K(x) be such that for any ...

A polynomial map phi_(f), with f=(f_1,...,f_n) in (K[X_1,...,X_n])^m in a field K is called invertible if there exist g_1,...,g_m in K[X_1,...,x_n] such that ...

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

The prime subfield of a field F is the subfield of F generated by the multiplicative identity 1_F of F. It is isomorphic to either Q (if the field characteristic is 0), or ...

The doublestruck letter R denotes the field of real numbers.

A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

A unit in a ring is an element u such that there exists u^(-1) where u·u^(-1)=1.

Deciding whether a given Boolean formula in conjunctive normal form has an assignment that makes the formula "true." In 1971, Cook showed that the problem is NP-complete.

Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and (A+B)/B=A/(A ...

A polynomial equation whose roots all have negative real parts. For a real quadratic equation z^2+Bz+C=0, the stability conditions are B,C>0. For a real cubic equation ...