Monomial ideal
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.
See also
- Graph ideal
- Stanley–Reisner ring
- A-hypergeometric function
- Hodge algebra
References
- D. Cox, Lectures on toric varieties, Lecture 3. § 4 and § 5.
- Sturmfels, B. (1996) Gröbner Bases and Convex Polytopes. American Mathematical Society, Providence
- D. Taylor, Ideals generated by monomials in an R-sequence, Ph. D. thesis, University of Chicago, 1966.
- B. Teissier, Monomial Ideals, Binomial Ideals, Polynomial Ideals, 2004
This article is issued from
Wikipedia.
The text is licensed under Creative Commons - Attribution - Sharealike.
Additional terms may apply for the media files.