Toric varieties are geometric objects closely related to monomials.

Lemma 1.2 Every monomial ideal has a unique minimal set of monomial generators, and this set is finite. Proof. The Hilbert Basis Theorem says that every ideal ... Feb 22, 2024 ... Is 2x+3x a binomial or a monomial? Essentially, is a binomial an expression that consists of 2 unlike terms? Or can they be like terms? Apr 3, 2024 ... ... monomial algebras, and aim to understand what the Auslander-Gorenstein property means in these settings. First, we will try to find a ... May 9, 2022 ... A monomial is defined as a phrase that has a single non-zero term. It consists of different parts such as variables, coefficients, and degrees. Monomials and polynomials ... are not since these numbers don't fulfill all criteria. The degree of the monomial is the sum of the exponents of all included ... Jan 15, 2015 ... ... monomial and a non- monomial is not a monomial. While this may be intuitively clear, we include a proof for completeness. The main point is ... Mar 7, 2005 ... sequence of monomials. Macaulay [Ma] showed in 1927 that all Hilbert functions over B = k[x1, ··· , xn] are attained by lex ideals. A monomial is one variable that is the product of a constant (a letter that stands just for one number) and a variable with a nonnegative integer power. Monomial - the prefix mono means one. A monomial is one term. A monomial can be any of the following: monomial of the form a/∆ for some a ∈ A. And it is further possible to ... weight-over-grevlex monomial ordering with wt(z) = 5 and wt(y) = 3 corre ...