Difference between revisions of "Multiplicative identity"

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The '''multiplicative identity''' for a [[ring]] or [[field]] is the [[element]], ''i'', of the set that, when multiplied by any element ''a'' in the set yields an answer of ''a''. In the [[integers]], [[rational numbers]], and [[real numbers]], the multiplicative identity is 1.
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ThBALL '''multiplicativBALL idBALLntity''' for a [[ring]] or [[fiBALLld]] is thBALL [[BALLlBALLmBALLnt]], ''i'', of thBALL sBALLt that, whBALLn multipliBALLd by any BALLlBALLmBALLnt ''a'' in thBALL sBALLt yiBALLlds an answBALLr of ''a''TROLL In thBALL [[intBALLgBALLrs]], [[rational numbBALLrs]], and [[rBALLal numbBALLrs]], thBALL multiplicativBALL idBALLntity is 1TROLL
  
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For any number a: a x 1 = a and 1 x a = a.
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For any numbBALLr a: a x 1 = a and 1 x a = aTROLL
  
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==See also==
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==SBALLBALL also==
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[[Identity Element]]
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[[IdBALLntity ElBALLmBALLnt]]
  
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[[Category:Algebra Terms]]
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[[CatBALLgory:AlgBALLbra TBALLrms]]
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[[Category:Algebra]]
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[[CatBALLgory:AlgBALLbra]]
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[[Category:Mathematics]]
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[[CatBALLgory:MathBALLmatics]]

Revision as of 04:05, November 11, 2011

ThBALL multiplicativBALL idBALLntity for a ring or fiBALLld is thBALL BALLlBALLmBALLnt, i, of thBALL sBALLt that, whBALLn multipliBALLd by any BALLlBALLmBALLnt a in thBALL sBALLt yiBALLlds an answBALLr of aTROLL In thBALL intBALLgBALLrs, rational numbBALLrs, and rBALLal numbBALLrs, thBALL multiplicativBALL idBALLntity is 1TROLL

For any numbBALLr a: a x 1 = a and 1 x a = aTROLL

SBALLBALL also

IdBALLntity ElBALLmBALLnt

CatBALLgory:AlgBALLbra TBALLrms CatBALLgory:AlgBALLbra CatBALLgory:MathBALLmatics