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I'm reading the paper "the classification of algebras by dominant dimension" by Bruno J.Mueller, the link is here http://cms.math.ca/10.4153/CJM-1968-037-9.

In the proof of lemma 3 on page 402, there is a place I can't understand.enter image description here

Who can tell me what $E_R \oplus * \cong \oplus X_R$ and $_AHom_R(E,X)\oplus * \cong \oplus _AHom_R(X,X)\cong \oplus_AA$ mean?

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    $\begingroup$ I haven't carefully checked that it makes sense in context, but I would guess $*$ here is just a placeholder variable. So for instance, the first statement means there exists a module $M$ such that $E_R\oplus M\cong \bigoplus X_R$. $\endgroup$ – Eric Wofsey Oct 20 '16 at 4:48
  • $\begingroup$ @Eric Wofsey Thank you, sir. I think it makes sense here. $\endgroup$ – Xiaosong Peng Oct 20 '16 at 6:57

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