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A three-dimensional shadow of a four-dimensional Klein bottle.

Let K be a number field with ring of integers R and let A be a nontrivial ideal of R. Then the ideal class of A, denoted [A], is the set of fractional ideals B such that ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

The ideal quotient (a:b) is an analog of division for ideals in a commutative ring R, (a:b)={x in R:xb subset a}. The ideal quotient is always another ideal. However, this ...

The multiplicative subgroup of all elements in the product of the multiplicative groups k_nu^× whose absolute value is 1 at all but finitely many nu, where k is a number ...

A periodic matrix with period 1, so that A^2=A.

A quantity which rigorously assumes the value of zero is said to be identically zero. The "identically" is used for emphasis when simply stating that a quantity is (or ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

The operator I^~ which takes a real number to the same real number I^~r=r.