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The algebra A is called a pre-C^*-algebra if it satisfies all conditions to be a C^*-algebra except that its norm need not be complete.

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

Let alpha be a nonzero rational number alpha=+/-p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L), where p_1, ..., p_L are distinct primes, alpha_l in Z and alpha_l!=0. Then ...

The quantity ps-rq obtained by letting x = pX+qY (1) y = rX+sY (2) in ax^2+2bxy+cy^2 (3) so that A = ap^2+2bpr+cr^2 (4) B = apq+b(ps+qr)+crs (5) C = aq^2+2bqs+cs^2 (6) and ...

The unit fraction 1/4, also called one-fourth. 1/4 is a rational number with terminating decimal expansion 0.25.

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A function is termed regular iff it is analytic and single-valued throughout a region R.

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

There is a one-to-one correspondence between the sets of equivalent correspondences (not of value 0) on an irreducible curve of curve genus p, and the rational collineations ...