- #1
Artusartos
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"Let R be a commutative ring. We say that M is an algebra over R, or that M is an R-algebra if M is an R-module that is also a ring (not necessarily commutative), and the ring and module operations are compatible, i.e., [tex]r(xy) = (rx)y = x(ry)[/tex] for all [itex]x, y \in M[/itex] and [itex]r \in R[/itex]."
I'm not really sure why the second equality is true, because it implies commutativity and the definition tells us that an R-module is not necessarily commutative, right?
Thank you in advance
I'm not really sure why the second equality is true, because it implies commutativity and the definition tells us that an R-module is not necessarily commutative, right?
Thank you in advance