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@Taneb Taneb commented Nov 3, 2025

On top of #2855, taken from #2729

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jamesmckinna commented Nov 3, 2025

As with the (admittedly fiddly) factorisation of the Binomial Theorem in #1928 , consider refactoring this so that:

  • the principal ideal of a general Ring is well-defined for any element which commutes with everything in the ring
  • hence, for a CommutativeRing, the principal ideal is always well-defined.

UPDATED: might usefully need to define the Centre Center of an algebra, commutator subgroup of a group, ... etc. as free-standing concepts, for subsequent (refactored) deployment in this context? #2863 / #2873

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Taneb commented Nov 3, 2025

As with the (admittedly fiddly) factorisation of the Binomial Theorem, consider refactoring this so that:

* the principal ideal of a general `Ring` is well-defined for _any_ element which commutes with everything in the ring

* hence, for a `CommutativeRing`, the principal ideal is _always_ well-defined.

To help justify this to future me who may have forgotten this, the scalar multiples of the identity matrix commute with all square matrices (over a commutative ring)

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I know it's still draft, I'm still approving!

@Taneb Taneb force-pushed the quotient-rings branch 2 times, most recently from df16429 to e18c588 Compare November 10, 2025 10:36
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4 participants