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arXiv · 2610.23129

A prime isoartinian ring that is not noetherian

Zahra Nazemian·Doniyor Yazdonov
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Abstract

A right module is isoartinian (resp., isonoetherian) if every descending (resp., ascending) chain of submodules is eventually constant up to isomorphism, and a ring R is right isoartinian (resp., isonoethe- rian) if RR is isoartinian (resp., isonoetherian). Facchini and Nazemian proved that a semiprime right isoartinian ring is right noetherian if and only if it is right isonoetherian if and only if it has finite Goldie dimen- sion and that every commutative semiprime isoartinian ring is noether- ian. We construct, over an arbitrary field K, a (non commutative) prime (right and left) isoartinian ring that is neither right nor left noetherian.

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Zahra Nazemian, Doniyor Yazdonov. 2026-10-16. A prime isoartinian ring that is not noetherian. https://arxiv.org/abs/2610.23129

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