[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.