Examples
Denote Q the rational number field. In Q with variable ordering x1 < x2 < x3,
is a triangular set and also a regular chain. Two generic points given by T are (a, a, a) and (a, -a, a) where a is transcendental over Q. Thus there are two irreducible components, given by { x2 - x1, x3 - x1 } and { x2 + x1, x3 - x1 }, respectively. Note that: (1) the content of the second polynomial is x2, which does not contribute to the generic points represented and thus can be removed; (2) the dimension of each component is 1, the number of free variables in the regular chain.
Read more about this topic: Regular Chain
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