Category theory has the concept of a groupoid and this is a different concept from the use of the word groupoid to refer to a magma.
Wikipedia gives an algebraic definition of this concept of groupoid as a set with a partial binary function.
A ringoid is described as a “ring with many objects”.
What is an algebraic definition of a ringoid along the same lines as the algebraic definition of a groupoid given by Wikipedia? Is it just a ring in which the addition is only partially defined, or is the multiplication also only partially defined?