quotient module - перевод на русский
Diclib.com
Словарь ChatGPT
Введите слово или словосочетание на любом языке 👆
Язык:

Перевод и анализ слов искусственным интеллектом ChatGPT

На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:

  • как употребляется слово
  • частота употребления
  • используется оно чаще в устной или письменной речи
  • варианты перевода слова
  • примеры употребления (несколько фраз с переводом)
  • этимология

quotient module - перевод на русский

ALGEBRAIC CONSTRUCTION
Factor module

quotient module         

общая лексика

фактор-модуль

factor module         

общая лексика

фактор-модуль

left module         
GENERALIZATION OF VECTOR SPACE, WITH SCALARS IN A RING INSTEAD OF A FIELD
Module (algebra); Submodule; Module theory; Submodules; R-module; Module over a ring; Left module; Module Theory; Unital module; Module (ring theory); Right module; Left-module; Module mathematics; Ring action; Z-module; ℤ-module

математика

левый модуль

Определение

module
¦ noun each of a set of standardized parts or independent units that can be used to construct a more complex structure.
?each of a set of independent units of study or training forming part of a course.
?an detachable self-contained unit of a spacecraft.
Origin
C16: from Fr., or from L. modulus (see modulus).

Википедия

Quotient module

In algebra, given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a quotient vector space. It differs from analogous quotient constructions of rings and groups by the fact that in these cases, the subspace that is used for defining the quotient is not of the same nature as the ambient space (that is, a quotient ring is the quotient of a ring by an ideal, not a subring, and a quotient group is the quotient of a group by a normal subgroup, not by a general subgroup).

Given a module A over a ring R, and a submodule B of A, the quotient space A/B is defined by the equivalence relation

a b {\displaystyle a\sim b} if and only if b a B , {\displaystyle b-a\in B,}

for any a, b in A. The elements of A/B are the equivalence classes [ a ] = a + B = { a + b : b B } . {\displaystyle [a]=a+B=\{a+b:b\in B\}.} The function π : A A / B {\displaystyle \pi :A\to A/B} sending a in A to its equivalence class a + B is called the quotient map or the projection map, and is a module homomorphism.

The addition operation on A/B is defined for two equivalence classes as the equivalence class of the sum of two representatives from these classes; and scalar multiplication of elements of A/B by elements of R is defined similarly. Note that it has to be shown that these operations are well-defined. Then A/B becomes itself an R-module, called the quotient module. In symbols, for all a, b in A and r in R:

( a + B ) + ( b + B ) := ( a + b ) + B , r ( a + B ) := ( r a ) + B . {\displaystyle {\begin{aligned}&(a+B)+(b+B):=(a+b)+B,\\&r\cdot (a+B):=(r\cdot a)+B.\end{aligned}}}
Как переводится quotient module на Русский язык