show that the ring of complex umbers (+) Can be imbedding a ring of 2x2 matrics (M ₂x₂ 2X2
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- [Type here] 15. Give an example of an infinite commutative ring with no zero divisors that is not an integral domain. [Type here]22. Let be a ring with finite number of elements. Show that the characteristic of divides .Prove that if a subring R of an integral domain D contains the unity element of D, then R is an integral domain. [Type here][Type here]
- Consider L ∞[−1, 1] with the essential sup-norm (see Definition3.2.12). Show that the essential sup-norm cannot be induced by an inner product.Show that the union of a chain I1 ⊂ I2 ⊂ .... of ideals of a ring R isan ideal of R.Prove theorem 16.41, using the attached definition of quotient rings. Thanks!