{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/absorbing-ideals-a-survey-on-o-stable-groups","title":"Absorbing ideals: a survey on $ω$-stable groups","arxiv_id":"2401.12766","date":"2024-01-20","proceeding":null,"authors":["Bruno Moreira Fernandes"],"abstract":"We introduce a new concept in the Absorbing Ideal Theory in commutative rings, that is, the $\\omega$-stable groups. We will provide examples and non-examples of these groups, and establish their relationship with H-congruence. Ultimately, we will study the action of these groups considering the transitivity condition","url_abs":"https://arxiv.org/abs/2401.12766v1","url_pdf":"https://arxiv.org/pdf/2401.12766v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"absorbing-ideals-a-survey-on-o-stable-groups","repo_url":"https://github.com/brmoreirafer/Aborbing-Ideal-Theory","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}