Results 1 to 2 of 2

Math Help - what is algebra?

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    2

    what is algebra?

    sorry before.
    close this thread if it doesn't belong there

    it is known, abstract algebra studying about algebraic structure. algebraic structure is non-empty set with one or more binary operation and satisfy some axioms. for example group,ring,field,etc.

    its often write "let R be an algebra with relation...." or "let R be an algebra over field S"
    what the meaning of algebra? what's the different from algebraic structure?

    question: let R be algebra over field Q (rational), with relation r=\frac{r^{n}}{n!} n element of natural number. R is a ring or not??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,319
    Thanks
    697

    Re: what is algebra?

    you may be referring to an algebra over a field, which has a dual structure as a ring and a vector space, which share the same additive operation. for compatability reasons, the multiplication is required to be bilinear (so it satisfies the distributive laws). the usual examples are associative and unital (the ring has unity), but other examples do exist.

    some typical examples of such algebras are: nxn matrices over a field, polynomials over a field (F[x]), and the quaternions. for any vector space V, the set End(V) = Hom(V,V) is another example (in which the multiplication is function composition).

    as a vector space, we can consider such things as dim(A), bases, and scalar multiples. as a ring we can talk about ideals, and the group of units (the group of units of the algebra of nxn matrices is the general linear group of degree n over F).

    i'm not sure what you are trying to ask with the specific relation in your question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 4th 2011, 08:39 AM
  2. Replies: 2
    Last Post: December 6th 2010, 03:03 PM
  3. Algebra or Algebra 2 Equation Help Please?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 12th 2010, 11:22 AM
  4. Replies: 0
    Last Post: April 23rd 2010, 11:37 PM
  5. algebra help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 20th 2007, 10:33 AM

Search Tags


/mathhelpforum @mathhelpforum