3 ms·

What's wrong with negative degree monomials?

• red_trumpet 4y ago
  You mean like $x^{-1} = 1/x$? That's called a rational function[1], but not a polynomial, so it's not an element of the polynomial ring[2]. Of course you can also consider the algebra of rational functions, but this is a field[3] (almost by definition: you make every polynomial invertible), which means that modding out anything other than 0 yields the zero ring[4]. [1] https://en.wikipedia.org/wiki/Rational_function https://en.wikipedia.org/wiki/Rational_function [2] https://en.wikipedia.org/wiki/Polynomial_ring https://en.wikipedia.org/wiki/Polynomial_ring [3] https://en.wikipedia.org/wiki/Field_(mathematics) https://en.wikipedia.org/wiki/Field_(mathematics) [4] https://en.wikipedia.org/wiki/Zero_ring https://en.wikipedia.org/wiki/Zero_ring