Re: Irreducibles (Ring theory )

In article <d5bhpc$ecr$2@xxxxxxxxxxxxxxxxxx>, po <po@xxxxxx> wrote:
>Im trying to understand what an irreducible element is.
>i have my definition
>an element (r) is irreducible if
>it is not equal to 0
>r is not invertible r=ab a or b is invertible

These are THREE conditions. r is irreducible if and only if:

(i) r is not equal to 0; and
(ii) r is not invertible; and
(iii) For ALL a and b, if r=ab, then either a is invertible or b is invertible.

>then in a text book i have the irreducibles of the integers are all the
>prime numbers and their negatives...
>but what about the other numbers? whats the inverse of 4? (in the integers,
>it doesnt exist, so why is this not an irreducible?)

Because it fails to satisfy the third condition: 4 = 2*2, but 2 is not
invertible.




--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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