Bill Dubuque <wgd@[EMAIL PROTECTED]
> wrote:
>Someonekicked <atouiahmad@[EMAIL PROTECTED]
> wrote:
>>
>> ... questions about lines over Z/n ...
>
> Over a field any of the usual normal forms for lines may be employed.
> However, if n isn't prime then Z/n isn't a field and this breaks down.
> E.g. in Z/15 the lines y = 0, 3x = 5y both pass through (0,0), (5,0)
> but (5,3) is on the latter but not the former. So over a non-field ring
> a line is no longer uniquely determined by two distinct points on it.
Linear algebra over rings (vs. fields) is known as module theory, i.e.
an R-module is the structure obtained by generalizing a vector space
to allow coefficients from the ring R. As we saw above, many of the
familiar vector space theorems fail for general modules. You can find
introductions to module theory in many abstract algebra textbooks.
--Bill Dubuque
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