symmetric monoidal (∞,1)-category of spectra
A rng (terminology due to Jacobson) is a ring ‘without identity’ (hence the missing ‘i’ in the name, get it?). By the red herring principle, we sometimes speak of a nonunital ring. Note that classically, the word ‘ring’ originally meant a rng, but we usually require our rings to have identities.
Specifically, a rng is a set with operations of addition and multiplication, such that:
A survey of commutative rng theory is in
The notation “rng” originates in
where the term is attributed to Louis Rowen.
(Bourbaki 6, chapter 1) uses the term “pseudo-ring” instead, which however has not caught on and even if more sane, will be understood less than “rng”.