Ideal in a variety with zero
Let be a variety of algebras with zero. In other words, has an operator domain comprising operators with various arities, some universal identities satisfied by these operators, and a distinguished constant operator among these, called the zero operator.
Suppose is an algebra in . An ideal in is a subset containing zero, with the following property:
For any expression constructed using the operators of the operator domain, such that whenever all the s are zero, takes the value zero, it is true that when all the are in , takes a value inside .