[Aardwolf]

This is one of those things were better naming would make mathematics easier, imho. The words are just so random and inconsistent.

Example: Commutative and Abelian are synonyms, but there's "Commutative monoid" and "Abelian group". Why not use same adjective. But of course also the random bag of words that have nothing to do with the concept, like magma.

[kortex]

Could take a page out of the biologist's book. "what's this thing?" Transcriptase - enzyme (-ase) which transcribes - DNA to RNA. "What about this" Reverse transcriptase - does the reverse of transcriptase.

Angiotensin-converting enzyme - does exactly what it says on the tin. You can lex it even further:

- Angio - heart (from ango, vessel)

- Tens - from hypertension, vis tendo, tendere, to stretch.

- (-in) - suffix associated with polypeptides:

- Convertere - turn around, from:

- Con - with

- Vert - turn

- En - inside

- Zyme - from zume/zymē - leavened, loosely, biological thing which causes leavening

It just makes so much sense! Lexemes are so cool. Like digging into linguistic source code.

[avmich]

We suffer here from lack of classical education. Greek and Latin would probably help.

[QuesnayJr]

How did they get people to agree to it? Mathematical terminology is a crime, but the problem is that it's very hard to get people to coordinate on different terminology.

[zodiac]

Why not call the DNA to RNA enzyme reverse transcriptase and the RNA to DNA one transcriptase?

[QuesnayJr]

Commutative and abelian aren't really synonyms. "Abelian" is reserved for objects that have a certain amount of rigidity. Commutative monoids are squishy, while abelian groups very rigid. Another place you'll see the name "abelian" is "abelian Lie algebras", which are also rigid. "Abelian categories" axiomatize the kind of rigidity abelian groups have.

Magmas are usually called "groupoids", but there's another generalization of group also called "groupoids". I'm actually not sure they really deserve a short name, rather than just "set with a binary operation", since there isn't much you can say about them in that generality that you can't generalize to "set with two binary operations", "set with a binary and a trinary operation", etc. The argument for a name is it gives you something to modify, since there are interesting special cases such as "medial groupoids". (An example of a medial groupoid is the real numbers with the "average of two numbers" operation.)

[gugagore]

https://en.wikipedia.org/wiki/Rng_(algebra) is a small example of trying to use more consistent names, but it's too punny for my taste... (Rng is a ring without an identity element)

[rbonvall]

There's also a rig (a ring without "n"egatives): https://ncatlab.org/nlab/show/rig

I agree. Too cute for its own sake.