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- Jun 22, 2012

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

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

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

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

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I am somewhat overwhelmed by this problem and, at the very least, need some help to get started

Peter

This has also been posted on MHF

Peter