A note on connected reduced rings. (English) Zbl 1481.13016

This short note illustrates a constructive proof of a characterisation of reduced and connected rings, whereas the cassical proof makes an apparently fundamental use of prime ideals and Krull’s Lemma.
Avoiding these constructively non-admissible tools has been achieved by using instead radical ideals and their properties, which are constructively acceptable.
The most interesting part of the paper is Section 3, which provides a precise yet intuitive insight on the reasons why the approach works and thus how it can be applied on other problems.
For a reader who does not have already in mind the specific literature, the article could be hard to read since it heavily relies on the cited works, in particular [S. McAdam and R. G. Swan, Lect. Notes Pure Appl. Math. 236, 411–424 (2004; Zbl 1080.13002)]. Hence, it is recommended to read the paper together or after [loc. cit.], so that the neat and clean exposition of the note is appropriately complemented by the background in the latter work.


13B25 Polynomials over commutative rings
03F65 Other constructive mathematics


Zbl 1080.13002
Full Text: DOI Link


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