Find the dimension of

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- March 16th 2011, 03:59 PMhurle32Dimension of Factor Ring
Find the dimension of

- March 16th 2011, 10:58 PMNonCommAlg
if by "dimension" you mean dimension as a vector space over , the answer is . this is easy to see: put and and let be the ideal of which is generated by and . show that and conclude that is an -basis for your ring.

- March 16th 2011, 11:16 PMhurle32
I get everything up to the last conclusion: why does imply that is a basis?

Thanks! - March 16th 2011, 11:35 PMNonCommAlg
and so every element of your ring is in the form , for some also, since , we have , for some so generates your ring. it is obvious that the set is -linearly independent.