Definition talk:Module

Left vs. right modules
Hello. Should a distinction be made between left $R$-modules and right $R$-modules? --Jshflynn 18:34, 2 August 2012 (UTC)


 * I haven't seen this distinction made in any of the literature I've encountered. I can imagine what a right module is but apart from noting that every left module is trivially isomorphic to every right module (and therefore ultimately "the same thing") I can't immediately off the top of my head see why one would bother to design it. --prime mover 19:02, 2 August 2012 (UTC)


 * Yeah. It's probably the gentlest way to introduce an antihomomorphism (or more accurately an antiautomorphism) to someone but other than that... --Jshflynn 19:16, 2 August 2012 (UTC)


 * Yes, they are useful and one proves nontrivial things with them (e.g. existence of injectives, also in the commutative case). --barto (talk) (contribs) 12:06, 22 December 2017 (EST)

Rename to "module over ring"?
"Module" is more generally used for anything on which something acts (in this case: a ring action). We have Definition:G-Module, but there is much more, and they are referred to simply as "modules". Should this page be renamed to "R-Module" or "Module over Ring"? --barto (talk) (contribs) 12:06, 22 December 2017 (EST)


 * There's already an "also known as". --prime mover (talk) 12:31, 22 December 2017 (EST)


 * Further thought: as long as we don't make "module" a disambiguation page, we can possible transclude "R-Module" and "G-Module" as subpages of a more general "Module" page. If there then proves to be a definition of "module" which is a completely different concept, then we can rethink how we present it. --prime mover (talk) 12:48, 22 December 2017 (EST)