Inclined body

Inclined body

affects the special fields

is special case of

enclosure as special cases

an inclined body or a division ring (not identical to the term division algebra) is a quantity of S with two linkages“+” and”·“, which possesses all characteristics of a body, except that the multiplication it is not necessarily commutative.

An inclined body is thus a ring with one element <math> 1 \ neq0< /math>, in each element <math> the A \ neq0< /math> an inverse <math> a^ {- 1}< /math> possesses, so that <math> A cdot \ cdot a^ {- 1} =a^ {- 1} \ A = 1 </math>.

Examples of not commutative inclined bodies:

quaternions one show that each finite inclined body is a body (sentence of Wedderburn); not-commutative inclined bodies must be thus infinite.

 

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