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Math Help - Notation help

  1. #1
    Junior Member
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    Notation help

    I know the definition of a field but I haven't really studied much algebra. Can someone tell me what this means:

    \mathbb{F}_2[x,y]/(x^r,y^s)

    I know it involves a 2-element field but that's about it.
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  2. #2
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    it's a quotient ring. the "main ring" is the ring of polynomials in x and y, with coefficients in the 2-element field F2 = {0,1}. that ring is being factored via the ideal generated by two polynomials x^r and y^s (that is, any polynomial of the form p(x,y)x^r + q(x,y)y^s is treated as if it was 0, so basically this knocks off all powers of x higher than r-1, and all powers of y higher than s-1).
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    It is the quotient ring R/I . In this case R is the ring \mathbb{F}_2[x,y] and I=(x^r.y^s) the ideal generated by x^r and y^s .



    Edited: Sorry, I didn't see Deveno's post.
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