数学Homework作业代写 MAT401 Homework 4

MAT401

数学Homework作业代写 These problems are due on Crowdmark by 6pm on Wednesday, March 2nd. The solutions will be discussed in tutorials that week.

Read: Gallian, Chapter 18 (Omit the material on Euclidean domains) and Chapter 20, pp338 –344.

You should also review Chapter 19, since we will assume this material on vector spaces is known.

These problems are due on Crowdmark by 6pm on Wednesday, March 2nd. The solutions will be discussed in tutorials that week.

Let R = Z[√−3]. Show that every element a ∈ R with a6= 0 and a not a unit is a product of irreducible elements. Note that we have seen that such a product is not unique.

Suppose that R is an integral domain with the property that every strictly decreasing chain of ideals 数学Homework作业代写

is fifinite. Show that R is a fifield. 数学Homework作业代写

(i) Show that the fifield Q(α) ⊂ R is isomorphic to

(ii) Show that Q(α) is not a splitting fifield of

(ii) Show that the polynomials have the same splitting fifield over Q

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