## The New Encyclopędia BritannicaEncyclopędia Britannica, 1983 - Encyclopedias and dictionaries |

### From inside the book

Results 1-3 of 84

Page 536

It is easy to show that the characteristic of any

former case, the prime subring ZP is already a

the latter case the prime subring Z can be (uniquely) extended to its

It is easy to show that the characteristic of any

**field**F is a prime p or infinity. In theformer case, the prime subring ZP is already a

**field**(i.e., closed under division). Inthe latter case the prime subring Z can be (uniquely) extended to its

**field**of ...Page 539

More generally, this is true of any normal

adjunctions of roots a1/n of constants a already constructed. It follows that if a

polynomial equation pix) = 0 over a

...

More generally, this is true of any normal

**field**extension obtained by successiveadjunctions of roots a1/n of constants a already constructed. It follows that if a

polynomial equation pix) = 0 over a

**field**F can be solved by radicals, in the sense...

Page 541

The

rational

in the following definition: Let F be any

...

The

**field**extension construction to be described gives the real**field**9? from therational

**field**Q; the complex**field**... of a Cauchy sequence, which is generalizedin the following definition: Let F be any

**field**with a real valuation <p satisfying the...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

accelerator acid activity Adams administrative advertising Aeschylus aesthetic Africa agriculture animals appear become body called Central century changes contains continued cost countries crops cultural dance early East effect electrons elements engineering established example farm feet field figures flight followed human important increase individual industry influence Italy Khoisan Knossos known Lake land languages later less living major materials means ment natural occur operations organization original patterns percent performance period plants play political population practice present production range region remains represented result River society sound South southern species structure style theory tion traditional United usually variety West Western widely