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m322qu2 - K with an appropriate scalar product If yes find...

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Spring 2009 Math 322 - Algebra II Quiz 2 - Vector Spaces Consider the ring R = ( Z 2 × Z 2 , + , · ) with the obvious addition and multiplication. (1) Is R commutative ring with identity? An integral domain? A Euclidean domain? Principal ideal domain? Unique factorisation domain? A field? (2) Can R be turned into a vector space with an appropriate choice of a field
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Unformatted text preview: K with an appropriate scalar product? If yes, find such a K . If no, prove that no such K exists. (3) Can you generalise your finding in part (2) to X = F × F with F an arbitrary field? (For R above, it is Z 2 ). Ferit ¨ Ozt¨urk, Bo˘ gazi¸ ci University 2009...
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