{"title":"From free idempotent monoids to free multiplicatively idempotent rigs","authors":"Morgan Rogers","doi":"arxiv-2408.17440","DOIUrl":null,"url":null,"abstract":"A multiplicatively idempotent rig (which we abbreviate to mirig) is a rig\nsatisfying the equation r2 = r. We show that a free mirig on finitely many\ngenerators is finite and compute its size. This work was originally motivated\nby a collaborative effort on the decentralized social network Mastodon to\ncompute the size of the free mirig on two generators.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.17440","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A multiplicatively idempotent rig (which we abbreviate to mirig) is a rig
satisfying the equation r2 = r. We show that a free mirig on finitely many
generators is finite and compute its size. This work was originally motivated
by a collaborative effort on the decentralized social network Mastodon to
compute the size of the free mirig on two generators.
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