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Split exact sequence
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<p>The term split exact sequence is used in two different ways by different people. Some people mean a <a href="/facts/Short_exact_sequence/leUJnwJb">short exact sequence</a> that right-splits (thus corresponding to a semidirect product) and some people mean a <a href="/facts/Short_exact_sequence/leUJnwJb">short exact sequence</a> that left-splits (which implies it right-splits, and corresponds to a direct product). This article takes the latter approach, but both are in common use. When reading a book or paper, it is important to note precisely which of the two meanings is in use. </p><p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a split exact sequence is a <a href="/facts/Short_exact_sequence/leUJnwJb">short exact sequence</a> in which the middle term is built out of the two outer terms in the simplest possible way. </p>