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Article #206

#206

From: herb
Date: Mon, 19 Apr 2004 13:40

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Hello,

I am confused relation between field and integral domain.
I know Every integral domain is a field.
Then, Is the converse of above : "Every finite field is integral domain"
true ?

My thinking is following:

 ________  Ring ______________________________________
|      ________ Ring with unity ___  __________________     |
|     |
|     |
|     |   ___ Division Ring ______  ________________    |     |
|     |  |                                                             |   |
|
|     |  |  ___ Integral domain_  ________________  |   |     |
|     |  | |                                                       |  |   |
|
|     |  | |   __ Finite field___   __Infinite field__   |  |   |     |
|     |  | |  |(=finite integral |  |                     |  |  |   |     |
|     |  | |  |   domain)       |  |                     |  |  |   |     |
|     |  | |   --------------     --------------   |  |  |     |
|     |   -|-----------------------------------|-    |     |
|     |     |___________________________________|     |     |
|     |___________________________________________|     |
|___________________________________________________|

Is above relation diagram correct ?

Thanks for any comments and any help !!

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From: "herb" <fuzzykyh@nate.com>
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Subject: Test
Date: Mon, 19 Apr 2004 22:40:06 +0900
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