List questions from direct-sum | MathQa

Direct sum counterexample

Published on 12 Jan 2025 - 21:55

Simultaneously diagonalize the regular representation of C2 (+) C2 (+) C2.

Published on 12 Jan 2025 - 23:34

Dual group of the direct sum of abelian groups

Published on 12 Jan 2025 - 21:54

Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?

Published on 03 Jan 2025 - 0:51

Let $φ: V→V$ be a linear map with $φ \circ φ = \text{id}$. If $U = \{v \in V | φ(v) = v\}, W = \{ v \in V | φ(v) = -v\}$. Prove $ V \cong U \oplus W$

Published on 12 Jan 2025 - 22:21

If $T:V\to V$ linear and $N(V)+R(T)=V$ then $V=N(T)\oplus R(T)$

Published on 12 Jan 2025 - 21:59

Free R-module as a direct sum of copies of R

Published on 12 Jan 2025 - 21:53

Projection of a vector onto direct sum subspace

Published on 12 Jan 2025 - 21:55

Question about equations involving sum of powers modulo a prime

Published on 12 Jan 2025 - 22:12

Splitting $\mathbb Z_{pq}$ into direct sum with $\mathbb Z_p$

Published on 12 Jan 2025 - 21:59