How are monomials used in the theory of singularities?

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 ... Yes, x y 2 is a monomial. A monomial is an algebraic expression that consists of one term. x y 2 is one term because it is the product of variables and/or ... 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. Let J ⊂ R a monomial ideal minimally generated by monomials. µ1,...,µr . For all subset σ ⊂ {1,...,r} we define the monomial. µ(J,σ) := lcm(µi |i ∈ σ) ∈ R ... 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 ... monomial, or a monomial with any given pattern. Unfortunately, this expression is essentially problematic and infeasible to realize, because a polynomial ... ideal generated by monomials. Accordingly, a monomial algebra is ∆#-graded as well as -graded. 2.2. A resolution. A monomial algebra k∆\I has a natural ... Mar 12, 2025 ... When dividing monomials, we need to remember our exponent rules, specifically the rule xmxn=xm−n . This means that when bases raised to ... ... 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. “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 ...