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Thread: [SOLVED] Composition of mappings notation

  1. #1
    MHF Contributor Swlabr's Avatar
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    [SOLVED] Composition of mappings notation

    Does the order we write composition of mappings change if we are writing the mappings on the left instead of the right?

    For instance, are $\displaystyle (g \circ f)(x)$ and $\displaystyle (x)(f \circ g)$ equivalent in general?
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  2. #2
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    Quote Originally Posted by Swlabr View Post

    For instance, are $\displaystyle (g \circ f)(x)$ and $\displaystyle (x)(f \circ g)$ equivalent in general?
    yes. one reason for choosing this order, for example in ring theory, is to avoid dealing with the opposite ring. so if $\displaystyle f,g$ are maps from a module M to itself, i.e. $\displaystyle f,g \in End(M),$ then assuming $\displaystyle *$

    is the multiplication operation in the ring $\displaystyle (End (M))^{opp},$ then we have $\displaystyle f * g=g \circ f.$
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