Division algebra
In abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible. The multiplication operation of a division algebra is not assumed to be necessarily either commutative or associative.
Division algebra - Wikipedia Jump to content From Wikipedia, the free encyclopedia Algebra over a field with only invertible elements and zero In abstract algebra , a division algebra is, roughly speaking, an algebra over a field in which division , except by zero, is always possible. The multiplication operation of a division algebra is not assumed to be necessarily either commutative or associative. Definitions [ edit ] Formally, suppose that D is a non-zero algebra over a field . Then D is a division algebra if, for every element a in D and every non-zero element b in D , there exists preci
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