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Unique identity and inverse question.

  1. Sep 3, 2005 #1
    When we say that the identity and inverse element in a vector space is unique, does it mean that those elements are the same for all x in V? or does it mean that each x has its own unique identity or inverse element?

    moreover, is there a geometric way of explaning what a field is? because I got confused about the scalar multiplication of a vector space that b in F and c in V which give bc in V..

    and also, did anyone used Linear Algebra by Friedberg, Insel and Spense before? What do you think about the book?
  2. jcsd
  3. Sep 3, 2005 #2
    unique identity means the whole algebraic system (group, ring or field, etc) has exactly one element e with the property that ae = ea = a for EVERY a in the object you're interested in. same goes for 'unique inverse' & so on.
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