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What is a division ring?

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In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring in which every nonzero element a has a multiplicative inverse, i.e., an element x with a. read more

A division ring is a type of noncommutative ring under the looser definition where noncommutative ring refers to rings which are not necessarily commutative. Division rings differ from fields only in that their multiplication is not required to be commutative. read more

and $R$ is a division ring. NB: Note I've used the fact that $R$ is a finite-dimensional vector space over $k$ (see ca. (2)-(3)); I don't see how this can be avoided. End of Note. read more

Definition of DIVISION RING: A ring which, if zero is removed, is a group under multiplication, ie every non-zero element has an inverse. A commutative division ring is a field, read more

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