Changes between Initial Version and Version 1 of Ticket #23190, comment 27


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Timestamp:
08/13/17 22:46:34 (5 years ago)
Author:
mderickx
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  • Ticket #23190, comment 27

    initial v1  
    11I think the mathematical content of the statement if R -> S is injective then the quotient is, is no true. A counter example is for example
    2 `ZZ['x'].quo(2) == GF(2)['x']` which does not inject into ``QQ['x'].quo(2) == 0`. This example is not a pathology of 2 being in the constant field, it fails for any polynomial whose content is not a unit.
     2`ZZ['x'].quo(2) == GF(2)['x']` which does not inject into `QQ['x'].quo(2) == 0`. This example is not a pathology of 2 being in the constant field, it fails for any polynomial whose content is not a unit.
    33
    44A nice sufficient condition for injectivity is that the polynomial be monic (or more generally if its leading coefficient is a unit).