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In algebra, a monomial ideal is an ideal generated by some monomials in a polynomial ring over a field of several variables.

A toric ideal is an ideal generated by differences of monomials (provided the ideal is a prime ideal). An affine or projecrive 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.
See also

Graph ideal
Stanley–Reisner ring
A-hypergeometric function
Hodge algebra


D. Cox, Lectures on toric varieties, Lecture 3. § 4 and § 5.
Sturmfels, B. (1996) Gröbner Bases and Convex Polytopes. American Mathematical Society, Providence
B. Teissier, Monomial Ideals, Binomial Ideals, Polynomial Ideals, 2004

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