Mathematically speaking, you can always weaken axioms. However, there are some extra advantages that additive groups have that commutative semirings don't have (mainly 0, the additive identity).
That being said, there isn't anything prevent you from constructing the appropriate categories. It would be good to have a more specific use-case in mind, but that isn't necessary. However, one should be careful with the name because it would conflict with what "most" people would call an algebra (which is why we have MagmaticAlgebras). Best, Travis On Tuesday, March 12, 2024 at 2:57:29 AM UTC+9 anime...@iiits.in wrote: > Hello Sir, > > I was going through "Algebras" and I had a doubt. > Does MagmaticAlgebra and AssociativeAlgebra have to be implemented over > Ring only? > I went through internet and google uses rings to define those algebras, > but the axioms that those algebra follow (Unital, Associative) are also > preserved by commutative semirings. > Would it be good to define MagmaticAlgebra and AssociativeAlgebra over > other objects that follow those axioms too or come-up with alternative > Algebra? > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-gsoc+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-gsoc/16b92130-c54e-48a4-abe0-243a7f6bac60n%40googlegroups.com.
