Monomial representations arise naturally in this context.

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 ... A monomial, also called a power product or primitive monomial, [1] is a product of powers of variables with nonnegative integer exponents. “Mono” means one. When polynomials are classified on the basis of the number of terms, the polynomials with only a single term are called monomials. This single ... Note: Monomials are just math expressions with a bunch of numbers and variables multiplied together, and one way to compare monomials is to keep track of ... Abstract. We show that for every r ∈ Z>0 there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to ... Oct 22, 2024 ... PDF | The irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications ... 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 ideal of depth at most 2, to any monomial ideal in at most 3 variables, and to any monomial ideal which is generic with respect to one variable. Feb 6, 2024 ... When it comes to multiplying the fraction in the polynomial by the monomial ( which is one part of the original binomial) I always come up with the answer 0 to ... A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher ...