## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 254

Any set of elements in mathematics that has two laws of composition, addition

and

an additive group, and (2) with

...

Any set of elements in mathematics that has two laws of composition, addition

and

**multiplication**, such that ( 1 ) with addition as the law of combination it formsan additive group, and (2) with

**multiplication**is commutative and associative, and...

Page 283

In order to get a field containing 4—1 (that is, to be able to carry out addition,

subtraction,

numbers of the form x + yi = x+iy = x + yj—l were considered more generally.

In order to get a field containing 4—1 (that is, to be able to carry out addition,

subtraction,

**multiplication**, and division subject to the usual rules), all complexnumbers of the form x + yi = x+iy = x + yj—l were considered more generally.

Page 293

Thus, if a

specific condition of associativity (see 319) is to be defined on K", it is sufficient to

define the n2 products efij (1 < i, j < /?), because then products of //-tuples are ...

Thus, if a

**multiplication**distributive with respect to addition and satisfying aspecific condition of associativity (see 319) is to be defined on K", it is sufficient to

define the n2 products efij (1 < i, j < /?), because then products of //-tuples are ...

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