Talk:Basis of Free Module is No Greater than Generator

We try to avoid mathfrak on $\mathsf{Pr} \infty \mathsf{fWiki}$ because its appearance is ugly and difficult to read. An alternative notation to $\mathfrak m$ is therefore encouraged. --prime mover (talk) 06:38, 3 May 2017 (EDT)

Oh okay. I personally don't think it's ugly. FYI, \mathfrak is standard notation for Lie algebra's. --barto (talk) 06:56, 3 May 2017 (EDT)

Regrettably that is the case. If there is one case for a desperately needed updating to mathematical notation, this is it. Take this as one who was taught German as a child by a well-meaning but otherwise bletheringly senile teacher who insisted on using pre-WWI textbooks, and equally insisted that I reproduce the appalling black-letter script by hand. Seriously, if someone were to build a bonfire of books filled with this nauseatingly obnoxious script in it, I wouldn't make water over it. --prime mover (talk) 07:03, 3 May 2017 (EDT)

Page rename suggestion

Not necessarily less than, may be same size as. So, something else --prime mover (talk) 09:43, 29 July 2017 (EDT)

Some alternatives: not Greater than, at Most as Large as, Injects into. I find not Greater than a bit confusing because of the negation, so I prefer at Most as Large as. --barto (talk) 10:53, 29 July 2017 (EDT)

I have no such qualms about using "no greater" so that's what we use. --prime mover (talk) 11:09, 29 July 2017 (EDT)

Proposed change

This theorem is dependent on the theorem Maximal Ideal iff Quotient Ring is Division Ring which is not true.

I propose that the theorem be changed to a commutative ring in the premise and invoke the theorem Maximal Ideal iff Quotient Ring is Field.

The only theorem dependent on Basis of Free Module is No Greater than Generator is the theorem Bases of Free Module have Equal Cardinality where the premise already assumes a commutative ring. --Leigh.Samphier (talk) 22:50, 19 October 2018 (EDT)

Feel free to do whatever you need to. --prime mover (talk) 05:36, 20 October 2018 (EDT)