Noun
non-unit (plural non-units)
Alternative form of nonunit
If p is a nonzero non-unit, we say that p is a prime element if, whenever p divides a product ab, then p divides a or p divides b. Equivalently, an element p is prime if and only if the principal ideal (p) is a nonzero prime ideal. Source: Internet
The Jacobson radical of a ring consists of elements that satisfy a stronger property than being merely a non-unit – in some sense, a member of the Jacobson radical must not "act as a unit" in any module "internal to the ring." Source: Internet