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Specifically, we focus on arithmetic data types that contain an error value\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\bot\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            whose main purpose is to always return a value for division. To rings and fields, we add a division operator\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(x\/y\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            and study a class of algebras called\n            <jats:italic>common meadows<\/jats:italic>\n            wherein\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(x\/0=\\bot\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            . The set of equations true in all common meadows is named the\n            <jats:italic>equational theory of common meadows<\/jats:italic>\n            . We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable.\n          <\/jats:p>","DOI":"10.1145\/3689211","type":"journal-article","created":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T14:41:50Z","timestamp":1723905710000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["A Complete Finite Axiomatisation of the Equational Theory of Common Meadows"],"prefix":"10.1145","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2492-506X","authenticated-orcid":false,"given":"Jan A.","family":"Bergstra","sequence":"first","affiliation":[{"name":"Informatics Institute, University of Amsterdam, Amsterdam, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4689-8760","authenticated-orcid":false,"given":"John V.","family":"Tucker","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Swansea University, Swansea, Wales, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,11,13]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"649902","volume-title":"Proc. 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