If a ring R is Noetherian, then the ring of these objects over R is also Noetherian according to the Hilbert basis theorem.
If a ring R is Noetherian, then the ring of these objects over R is also Noetherian according to the Hilbert basis theorem. Given a set of these objects S, the set of values which make every element of S vanish is an affine variety. For a ring or a field denoted K, the ring of these objects over the ring or field is denoted K followed by x enclosed in brackets. A monic one of these objects whose roots are the eigenvalues of a matrix is the matrix's (*) "characteristic" one. Descartes' rule of signs applies to equations of these objects. Techniques for solving equations of these functions degree 2 include completing the square, factoring, and using the quadratic formula. For 10 points each, name these functions consisting of variables multiplied by coefficients and raised to integer exponents, such as "x squared minus four."
If a ring R is Noetherian, then the ring of these objects over R is also Noetherian according to the Hilbert basis theorem.
polynomials