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Math Help - [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 (g \circ f)(x) and (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 (g \circ f)(x) and (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 f,g are maps from a module M to itself, i.e. f,g \in End(M), then assuming *

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