In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions:[1] Connectedness defines a fairly general class of commutative rings.
In particular, all integral domains are connected.
Non-examples are given by product rings such as Z × Z; here the element (1, 0) is a non-trivial idempotent.
In algebraic geometry, connectedness is generalized to the concept of a connected scheme.
This commutative algebra-related article is a stub.