Monomial equations of the form $ax^n = c$ are often the first type encountered.

monomial module is an S-submodule of T which is generated by monomials xa ... monomial generating set which is either finite or forms a group under multiplication ... 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 ... It is important to understand when G is a Cohen-Macaulay ring, that is dim G = depthG; in this case, this is equivalent to (tg1 )∗ being a non-zerodivisor. Oct 25, 2007 ... In general, if we have N distinct monomials in a monomial support o geneous ideal I, then we would have at most [(N+1 )2j of them when co. 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 ... 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 ... May 19, 2006 ... ... monomial order γ, which is a total order on the monomials, compatible with the multiplication and such that 1 is smaller than any other monomial ... 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 ... Divide a polynomial expression by a monomial expression with rational number coefficients. Clarifications Clarification 1: Within the Algebra 1 course, ... Nov 13, 2011 ... So let's have a deeper look at what a monomial ordering is. Definition 1. Let N denote the non-negative integers. Let a = ( a 1 , ...