order number - ترجمة إلى الروسية
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order number - ترجمة إلى الروسية

CONCEPT IN RING THEORY
Maximal order; Order (number theory); Noncommutative number field

order number      

математика

порядковый номер

order number      
порядковый номер
multiplicative order         
Order in number theory; Multiplicative suborder; Order-finding problem

математика

мультипликативный порядок

تعريف

ВЕЩЕСТВЕННОЕ ЧИСЛО
то же, что действительное число.

ويكيبيديا

Order (ring theory)

In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that

  1. A {\displaystyle A} is a finite-dimensional algebra over the field Q {\displaystyle \mathbb {Q} } of rational numbers
  2. O {\displaystyle {\mathcal {O}}} spans A {\displaystyle A} over Q {\displaystyle \mathbb {Q} } , and
  3. O {\displaystyle {\mathcal {O}}} is a Z {\displaystyle \mathbb {Z} } -lattice in A {\displaystyle A} .

The last two conditions can be stated in less formal terms: Additively, O {\displaystyle {\mathcal {O}}} is a free abelian group generated by a basis for A {\displaystyle A} over Q {\displaystyle \mathbb {Q} } .

More generally for R {\displaystyle R} an integral domain contained in a field K {\displaystyle K} , we define O {\displaystyle {\mathcal {O}}} to be an R {\displaystyle R} -order in a K {\displaystyle K} -algebra A {\displaystyle A} if it is a subring of A {\displaystyle A} which is a full R {\displaystyle R} -lattice.

When A {\displaystyle A} is not a commutative ring, the idea of order is still important, but the phenomena are different. For example, the Hurwitz quaternions form a maximal order in the quaternions with rational co-ordinates; they are not the quaternions with integer coordinates in the most obvious sense. Maximal orders exist in general, but need not be unique: there is in general no largest order, but a number of maximal orders. An important class of examples is that of integral group rings.

أمثلة من مجموعة نصية لـ٪ 1
1. The de–Baathification program was issued as Coalition Provisional Authority Order Number 1 on May 16, 2003, by L.
2. But the US government said it had given assurances to the UK government that it would not make McKinnon subject to "Military Order Number One" which allows the US president to detain suspects indefinitely.
3. Mr McKinnon‘s defence lawyers also argue that the US has failed to give sufficient assurances that he will not be tried under "military order number one", which would allow him to be treated as a foreign terrorist, tried in a secret military tribunal and held in Guantánamo Bay.
4. Lomibao claimed that under General Order number 5 issued in the wake of Proclamation 1017, the PNP has a «clear mandate» to «carry out appropriate action and security measures to prevent an escalation of the situation.» While the military has crushed a plot to unseat Arroyo on Friday, Lomibao said «some people responsible for it are still out there.» Playing Favorites While saying his support for Arroyo was «waning,» Ramos’ statements yesterday showed a total withdrawal of support.
What is the الروسية for order number? Translation of &#39order number&#39 to الروسية