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A polynomial with three terms.

(x^2+axy+by^2)(t^2+atu+bu^2)=r^2+ars+bs^2, (1) where r = xt-byu (2) s = yt+xu+ayu. (3)

A polynomial in a single variable, e.g., P(x)=a_2x^2+a_1x+a_0, as opposed to a multivariate polynomial.

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

The p-layer of H, L_(p^')(H) is the unique minimal normal subgroup of H which maps onto E(H/O_(p^')(H)).

X is a p^'-group if p does not divide the group order of X.

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

The field F^_ is called an algebraic closure of F if F^_ is algebraic over F and if every polynomial f(x) in F[x] splits completely over F^_, so that F^_ can be said to ...

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.