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