Exercise 3, § 1

Algebra, X, p. 168

In the diagram of $A$ -modules :

\begin{array}{ccccc} &&P&\longleftarrow&M\\ &&\downarrow&\swarrow&\downarrow\\ &&N&\longleftarrow&Q \end{array} \qquad \begin{array}{c} \phantom{P}\\[-1.5em] \phantom{P}\!\!\!\!\!\!\!\!\!\!R \end{array}

does the commutativity of the two triangles extracted from the diagram necessarily imply that of the diagram?

Solution

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