Ring

A ring is an algebraic structure which is a generalisation of a field. That is, every field is a ring, as a field has additional restrictions.

Ambiguity of Definition

Unfortunately, for historical reasons, there is ambiguity over if a multiplicative identity is required in a ring. Hence the term ring may refer to either of the two disambiguating terms:

• non-unital ring (where no requirement for a multiplicative identity exists)
• ring with identity (which is guaranteed to have a multiplicative identity)

In the context of MATH3431, a ring refers to a non-unital ring.
In the context of MATH3711, a ring refers to a ring with identity.