A prime isoartinian ring that is not noetherian

@misc{nazemian2026prime,
  title = {{A prime isoartinian ring that is not noetherian}},
  author = {Zahra Nazemian and Doniyor Yazdonov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23129},
  eprint = {2610.23129},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23129},
}

TY  - UNPB
TI  - A prime isoartinian ring that is not noetherian
AU  - Zahra Nazemian
AU  - Doniyor Yazdonov
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23129
UR  - https://arxiv.org/abs/2610.23129
AB  - 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.
ER  -