The Wikipedia article is right for this term: polymerase chain reaction.
- An atomic reaction is a complex process. [general, indefinite]
Atomic reactions were studied by students during [whatever].
The atomic reaction of [whatever] was difficult to measure. [specific]
A polymerase chain reaction is a [whatever]; [singular, general, indefinite]
- EDIT: Polymerase chain reaction is [whatever]; singular, general, indefinite, non-countable. But it could take an A.
To describe a thing that is countable, use a or the plural of the noun.
- The polymerase chain reaction or reactions that occurred when [etc]; not general, specific.
- The indefinite article "a" is used for unspecified generalities.
- The plural of a countable noun is used for specified generalities.
In the first link from the OP:
Overlap extension represents a new approach to genetic engineering. Complementary
oligodeoxyribo-nucleotide (oligo) primers and the polymerase chain reaction are used to generate two DNA fragments having overlapping ends.
"the polymerase chain reaction" because for the author there is only one there: it is specific.
EDIT: It turns out that polymerase chain reaction is used by biologists as a non-count noun just like: nuclear fission or nuclear fusion.
I had no way of knowing until I read all about it. Now it makes sense. It would never be countable in biology and therefore would never take an s.