field of quotients
（ plural ）
Quizzes for review
(algebra) A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).
field of quotients
To construct the field of quotients from an integral domain, one represents each element as an equivalence class of ordered pairs (a,b) with b nonzero and defines addition by (a,b)+(a',b')=(ab'+a'b,bb') and multiplication coordinate-wise.
To construct the field of quotients from an integral domain, one represents each element as an equivalence class of ordered pairs (a,b) with b nonzero and defines addition by (a,b)+(a',b')=(ab'+a'b,bb') and multiplication coordinate-wise.
English - English
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
