Timeline for Terminology for certain monoids which are to monoids like fields are to rings
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2012 at 14:06 | comment | added | James Cranch | Because people who are new to this type of mathematics won't appreciate the right way of doing it unless someone takes the time to compare it to the wrong way now and again? | |
| Feb 10, 2012 at 15:13 | comment | added | Martin Brandenburg | I don't understand why such comments still arise today (and get upvotes), decades after universal algebra etc. has been established. Of course a homomorphism between monoids with zero is defined to be a map which preserves the whole structure, in particular the zero. There is no reason to apply the forgetful functor to monoids ... | |
| Feb 9, 2012 at 23:02 | comment | added | James Cranch | Of course, this functor is not quite an equivalence of categories, unless you demand that homomorphisms preserve zero. Otherwise, for example, there's an extra map between any two objects which sends everything (including the zero) to the identity. | |
| Feb 9, 2012 at 23:02 | comment | added | James Cranch | I agree it's clumsy, but I'm not wholly convinced you should disguise the characterisation. "Abelian groups with zero" is not all that long compared to some phrases in mathematics. | |
| Feb 9, 2012 at 23:01 | comment | added | James Cranch | (Edited to include the word "abelian"). | |
| Feb 9, 2012 at 22:58 | history | edited | James Cranch | CC BY-SA 3.0 |
added 8 characters in body
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| Feb 9, 2012 at 22:44 | comment | added | Martin Brandenburg | Isn't this just a bit clumsy, or rather a characterization? Namely, the functor $A \mapsto A^*$ establishes an isomorphism of categories between "field monoids" and abelian groups. | |
| Feb 9, 2012 at 20:01 | history | answered | James Cranch | CC BY-SA 3.0 |