Question

Abstract Algebra. Please explain everything in detail.

Step 1

To discuss the reason why the three given functions fail to satisfy the properties of a Euclidean norm.

Step 2

.Let D be a domain. A non-negative integer valued function N: D-{0} is Euclidean , if given a, b in D there exist q and r in D such that a=bq+r, with either r=0 or N(r)<N(b). Basically, the function N makes the Euclidean algorithm work in D.

Step 3

To show that f(x,y) going to highest degree in x is not a Euclidean function. (By symmetry) , the...

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