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**Unformatted text preview: **V be the set of all polynomials over Q of degree 3, together with the zero polynomial. Is V a vector space? Why or why not? 6. Recall that a ring homomorphism is one that preserves the operations of a ring, and that its kernel is an ideal. Dene a vector space analogue of a ring homomorphism, and show that its kernel is a subspace. 7. Show that Q ( i, 2) = Q ( i + 2 , 4- 32). 8. Is the extension Q ( + 1) of Q algebraic or transcendental? Is the extension Q ( ) algebraic or transcendental over the eld Q ( 3 )? (Note that Q ( 3 ) is indeed a subeld of Q ( ).) 1...

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