Changes between Initial Version and Version 1 of Ticket #23190, comment 27
- Timestamp:
- 08/13/17 22:46:34 (5 years ago)
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Ticket #23190, comment 27
initial v1 1 1 I 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. 3 3 4 4 A nice sufficient condition for injectivity is that the polynomial be monic (or more generally if its leading coefficient is a unit).