rng

A rng 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 $R$ with operations of addition and multiplication, such that * $R$ is a semigroup under multiplication; * $R$ is an abelian group under addition; * multiplication distributes over addition.

More sophisticatedly, we can say that, just as a ring is a monoid object in Ab, so a rng is a semigroup object in $Ab$.

Revised on June 19, 2014 08:32:35
by Colin Zwanziger
(74.92.19.28)