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Math Help - Matrix rings acting on right R-modules

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    Super Member Bernhard's Avatar
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    Matrix rings acting on right R-modules

    In the book "Modules and Rings" by John Dauns he adopts the following notation in Exercises 1-5 (see attached)

    "For additive groups A, B, C, D and  a \in A, b \in B, c \in C, d \in D we write

     [a,b; c,d] = \begin {vmatrix} a & b \\ c & d \end {vmatrix}  ;  [A, B, C, D] = \begin {vmatrix} A & B \\ C & D \end {vmatrix} "


    Exercise 1 (i), (ii) and (iii)

    The matrix ring R acts on the right R-module M whose elements are row vectors:

    Find (i) all submodules of M (ii) all right ideals of R, indicating which of these are ideals


     R = [ \mathbb{Z}_2, \mathbb{Z}_2; 0,  \mathbb{Z}_2, ] , M = \mathbb{Z}_2 \oplus \mathbb{Z}_2,

    -----------------------------------------------------------------------------------------------------------------------------------

    Would be most grateful for help

    Peter
    Last edited by Bernhard; August 9th 2013 at 07:42 PM.
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