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  2. Ring (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Ring_(mathematics)

    The term "Zahlring" (number ring) was coined by David Hilbert in 1892 and published in 1897. [13] ... The matrix ring of size n over a ring R will be denoted by R n.

  3. Ring size - Wikipedia

    en.wikipedia.org/wiki/Ring_size

    In Russia, ring sizes are equal to the inner diameter rounded to whole and half numbers, sometimes to quarters, for example diameter 16.92 mm is equal to size 17, 16.1 mm is equal to size 16. Equivalency table

  4. Quaternion - Wikipedia

    en.wikipedia.org/wiki/Quaternion

    The set A is a ring (in fact a domain) and a lattice and is called the ring of Hurwitz quaternions. There are 24 unit quaternions in this ring, and they are the vertices of a regular 24 cell with Schläfli symbol {3,4,3}. They correspond to the double cover of the rotational symmetry group of the regular tetrahedron.

  5. Ring theory - Wikipedia

    en.wikipedia.org/wiki/Ring_theory

    • Formal power series ring. Algebraic number theory • Algebraic number field • Integers modulo n • Ring of integers

  6. Module (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Module_(mathematics)

    Modules of this type are called free and if R has invariant basis number (e.g. any commutative ring or field) the number n is then the rank of the free module. If M n ( R ) is the ring of n × n matrices over a ring R , M is an M n ( R )-module, and e i is the n × n matrix with 1 in the ( i , i ) -entry (and zeros elsewhere), then e i M is an ...

  7. Ideal norm - Wikipedia

    en.wikipedia.org/wiki/Ideal_norm

    It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ideal in a less complicated ring. When the less complicated number ring is taken to be the ring of integers, Z, then the norm of a nonzero ideal I of a number ring R is simply the size of the finite quotient ring R/I.

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Algebraic variety - Wikipedia

    en.wikipedia.org/wiki/Algebraic_variety

    An affine algebraic set V is a variety if and only if I(V) is a prime ideal; equivalently, V is a variety if and only if its coordinate ring is an integral domain. [ 16 ] : 52 [ 1 ] : 4 Every nonempty affine algebraic set may be written uniquely as a finite union of algebraic varieties (where none of the varieties in the decomposition is a ...

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