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A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

Consider the forms Q for which the generic characters chi_i(Q) are equal to some preassigned array of signs e_i=1 or -1, e_1,e_2,...,e_r, subject to product_(i=1)^(r)e_i=1. ...

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A regular ring in the sense of commutative algebra is a commutative unit ring such that all its localizations at prime ideals are regular local rings. In contrast, a von ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♭. Then A is a right Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...