Complex sentence: More specifically, let M be any right R-module and N be any left R-module and we define A (m\\ otimes_R n) to be the free abelian group generated by pure tensors m\\ otimes_R n.
Split into simpler sentences: More specifically, let M be any right R-module and N be any left R-module. We first define A (m\\ otimes_R n) to be the free abelian group generated by pure tensors m\\ otimes_R n.