Talk:Irreducible element

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Zero divisors

Hello @D.Lazard: I am confused about your edit here: [1]. Irreducibility is defined also for (commutative) rings which are not integral domains, see for example [2] or [3], see also some research in this direction here [4]. Maximilian Janisch (talk) 10:30, 9 March 2023 (UTC)

To editor Maximilian Janisch: You are right that the definition can be (and has been) extended to any ring, including non-commutative ones. This nust be mentioned in the lead. However these extensions of the concept are not notable enough for WP. So, I have restored the previous definition (restricted to integral domains), added context explaining the importance of the context, and mentioned the possible extensions of the definitions. D.Lazard (talk) 14:51, 9 March 2023 (UTC)

@D.Lazard: Thank you for the information, the second paragraph that you added is quite interesting! I have added a bit more context on the difference between integral domains and commutative rings, cf. my latest edit. Meilleures salutations -- Maximilian Janisch (talk) 16:49, 9 March 2023 (UTC)