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Definition: A monomial is a formal product of some variables x_1, ... , x_n of the form ((x_1)^i_1)((x_2)^i_2)...((x_n)^i_n), where the exponents i_v are non-negative integers. The degree of a monomial, sometimes called the total degree, is the sum i_1 + ... + i_n.
Source: Algebra, second edition by Michael Artin