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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.

Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

The field of complex numbers, denoted C.

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.