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Abelian groups vs modules
Normally you'd call these abelian groups, or possibly Z-modules, because just calling them modules suggests things which aren't true. I suggest changing this to "abelian groups", which is what it would normally be called and what I've been calling it.
- genewardsmith July 31, 2012, 09:09:28 AM UTC-0700
OK, but what's the "dual group" of an abelian group? Is it well-defined?
- mbattaglia1 July 31, 2012, 09:15:56 AM UTC-0700
And what's the terminology I should use for the fundamental "spaces" in matrices then?
I see there's some precedence for talking about the "column module", "row module", "null module" of an integer matrix acting as a linear transformation on a Z-module, instead of column space, row space, etc. Would I call it the "column group" and "row group"? Would anyone know what I mean?
- mbattaglia1 July 31, 2012, 09:18:30 AM UTC-0700
Note also I explicitly spelled it out here at the top
But I'm curious what things I wrote aren't true of modules in general and only of Z-modules.
- mbattaglia1 July 31, 2012, 09:26:31 AM UTC-0700