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  • ...ction#The_Inverse_of_a_Function | inverse]] of a map <math>h</math> is the map <math>h^{-1}</math> given by <math>h^{-1}(a)=h(1-a)</math>. We can compose
    3 KB (479 words) - 14:35, 1 December 2015
  • * For some <math>0\in R</math>, <math>0+a=a+0=a</math> (existance of additive identity); ...ome <math>1\in R</math>, <math>1a=a1=a</math> (existance of multiplicative identity)
    6 KB (994 words) - 05:16, 8 April 2015
  • Indeed, the map <math>f:x\mapsto \gamma x</math> is an <math>R</math>-linear map from <math>I^{-1}\to I^{-1}</math>. As <math>R</math> is noetherian, <math> ...ath>, of <math>R</math> becomes an abelian group under multiplication. The identity element is <math>R</math> and the existence of inverses is guaranteed by th
    9 KB (1,648 words) - 15:36, 14 October 2017
  • ** (identity) For and object <math>X</math>, there is an identity morphism <math>1_X:X\to X</math> such that for any <math>f:A\to B</math>: < ...ect''' of all [[vector space|vector spaces]], where morphisms are [[linear map|linear maps]].
    5 KB (792 words) - 18:01, 7 April 2012
  • ...ing has additive identity <math>0=(0,0,0,\ldots)</math> and multiplicative identity <math>1 = (1,0,0,\ldots)</math>. ...a commutative ring <math>R</math>, one can define an <math>R</math>-linear map <math>\partial : R[x] \to R[x]</math> as follows:
    12 KB (2,010 words) - 23:10, 2 August 2020
  • ...ation <math>\cdot</math> makes <math>\pi_1(X,x_0)</math> into a group. The identity element is just the constant loop <math>e(a) = x_0</math>, and the inverse ...is a [[group homomorphism|homomorphism]]. Now we may similarly define the map <math>\varphi_{\bar\alpha}:\pi_1(X,x_1)\to\pi_1(X,x_0)</math> by <math>\var
    8 KB (1,518 words) - 19:11, 23 January 2017
  • ...ents in <math>B</math>, and each of the <math>4-x</math> elements in C can map to any of the <math>x</math> elements in B. This sum evaluates to <math>5(4 There is a total of 1 function (the identity) in this case.
    36 KB (6,214 words) - 19:22, 13 July 2023
  • ...n A</math> such that <math>ab=ba=1</math> (where 1 is the multiplicative [[identity]]). An element <math>p \in A</math> is [[prime]] if it is not zero, not a u ==The norm map==
    10 KB (1,646 words) - 14:04, 28 May 2020
  • ...that any combination involving two reflections across the x-axis would not map <math>T</math> back to itself. The same applies to two reflections across t ...ction twice, since that would give a net of no change and would require an identity rotation.
    8 KB (1,247 words) - 21:02, 30 October 2024