How does the concept of a monomial relate to special product formulas (e.g., $(a+b)^2$, $(a-b)^2$, $a^2-b^2$)?

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 ... May 2, 2016 ... Monomials are just the subset of polynomials having only one term. More plainly, a monomial is just a term. monomial self-map f : X X corresponds to a Z-linear map φ : N → N. See. Sections 1 and 2 for more details. We work in codimension 1 and say that f is 1 ... Jan 9, 2024 ... A monomial is a mathematical expression in algebra that consists of a single term. Unlike other algebraic expressions that might have multiple terms separated ... A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, eg, x, 3xy^2, or -2x^2y^3z. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank at most r. In ... Apr 29, 2021 ... That's just the definition of a monomial. It is a product of variables. A binomial is defined as the sum of two monomials, so as a, b are ... Jun 25, 2014 ... Abstract. This is a general talk in front of specialists on computational dif- ferential algebra. Monomials play a significant role in most ... Definition: Monomial. A monomial is a single-term algebraic expression that is the product of constants and variables, where the variables only have nonnegative ... “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 ...