| Version current |
Version 7 |
| A \emph{principal ideal domain} is an integral domain where every |
A \emph{principal ideal domain} is an integral domain where every |
| ideal is a principal ideal. |
ideal is a principal ideal. |
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| In a PID, an ideal $(p)$ is maximal if and only if $p$ is irreducible |
In a PID, an ideal $(p)$ is maximal if and only if $p$ is irreducible |
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(and prime since \PMlinkname{any PID is also a UFD}{PIDsAreUFDs}).
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(and prime since any PID is also a UFD).
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| Note that subrings of PIDs are not necessarily PIDs. (There is |
Note that subrings of PIDs are not necessarily PIDs. (There is |
| an example of this within the entry biquadratic field.) |
an example of this within the entry biquadratic field.) |
