What is the connection between the $\text{kernel} \,\,ker(f)$ and the $\text{kernel}\,\,Ker(f)$ of a homomorphism $f$?

I tried finding an explanation of $ker(f)$ vs capitalized $Ker(f)$

I know $ker(f)$ is the set of all elements mapped to the identity


Both $\ker f$ and $\mathrm{Ker} \ f$ are used by mathematicians to refer to the set of elements mapped to the identity. It's just a personal convention as to whether you prefer the notation to be capitalized or not. Same with $\mathrm{im} \ f$ vs. $\mathrm{Im} \ f$ or $\hom(G, H)$ vs. $\mathrm{Hom}(G, H)$ or really any other mathematics notation.

  • $\begingroup$ okay thanks, what an odd question to ask then. $\endgroup$ – all.over Feb 3 '15 at 5:50

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.