I am reading the book Elements of the Representation Theory of Associative Algebras: Volume 1.

I have a on page 77. In (d) of Lemma 2.2 on Page 77, it is said that $$ L_a=\sum_{\alpha: a\to b} \operatorname{Coker}(\psi_{\alpha}: M_b \to M_a). $$

I think that $L_a$ should be $$ L_a=\cap_{\alpha: a\to b} \operatorname{Coker}(\varphi_{\alpha}: M_b \to M_a). $$

Is this true? Thank you very much.enter image description here

  • $\begingroup$ Do you mean cokernel? $\endgroup$ – Jim Apr 28 '13 at 7:18
  • $\begingroup$ @Jim, yes. I will edit. $\endgroup$ – LJR Apr 28 '13 at 7:20

Neither intersecting nor summing different cokernels really makes much sense. Both those operations require that there is a larger space to do the intersection/summation in.

In this case what they mean is that $L_a = M_a/J_a$ where $J_a$ is defined in (c).


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