In algebra, a monomial ideal is an ideal generated by some monomials in a multivariate polynomial ring over a field.
A toric ideal is an ideal generated by differences of monomials (provided the ideal is a prime ideal). An affine or projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toric variety, possibly non-normal.
The computer algebra system Macaulay 2 has commands that handle monomial ideals.
References
Monomial ideal Wikipedia(Text) CC BY-SA