• anonymous
1. Let R be a ring. Recall that its center, denoted Z ( R ), is by definition the set of elements r ∈ R such that r · r 0 = r 0 · r for all r 0 ∈ R . (a) Let Z → R be the canonical homomorphism. Show that its image is contained in the center of R . (b) Let R = Mat n,n . Show that its center consists of scalar matrices (i.e., multiples of the identity matrix). 2. Let V be a vector space over k , and recall that T ( V ) = ⊕ i ≥ 0 T i ( V ), where T i ( V ) = V ⊗ ... ⊗ V | {z } i for i ≥ 1 and T 0 ( V ) = k . (a
Mathematics
• Stacey Warren - Expert brainly.com
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SOLVED
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