This seems a really simple way to remember which is which, but if it was right, I'd expect an equally base name for the one for Naturals than semiring ("rig" doesn't count). I think this is how it goes for operators:

semiring: $+ *$
e.g. Naturals, no inverses

ring: $+ - *$
e.g. Integers, semiring with additive inverse (enabling subtraction)

field: $+ - * /$
e.g. Rationals, ring with multiplicative inverse (enabling division)

Are there any wrinkles I've missed that mean this isn't quite right?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.