{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T17:29:50Z","timestamp":1649093390470},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1991,9]]},"abstract":"<jats:p> Let F<jats:sub>1<\/jats:sub>, \u2026, F<jats:sub>k<\/jats:sub> be finite fields with distinct characteristics. We give a finite set of equations which axiomatize the equational theory of F<jats:sub>1<\/jats:sub>, \u2026, F<jats:sub>k<\/jats:sub> and then use these axioms to find a finite set of AC-term rewrite rules which is complete for this theory. <\/jats:p><jats:p> This gives finite sets of complete AC-term rewrite rules for most instances of x<jats:sup>m<\/jats:sup> \u2248 x rings by adding new rules to the usual AC-term rewrite rules for commutative rings. The first case for which we do not find a complete set of AC-term rewrite rules is x<jats:sup>22<\/jats:sup> \u2248 x, and we doubt that such rules can be found. If R is a set of AC-term rewrite rules from which one can derive x(y + z) \u2192 xy + xz, then we show R cannot be complete for x<jats:sup>22<\/jats:sup> \u2248 x rings. <\/jats:p>","DOI":"10.1142\/s0218196791000249","type":"journal-article","created":{"date-parts":[[2004,11,25]],"date-time":"2004-11-25T12:12:21Z","timestamp":1101384741000},"page":"353-369","source":"Crossref","is-referenced-by-count":3,"title":["TERM REWRITE RULES FOR FINITE FIELDS"],"prefix":"10.1142","volume":"01","author":[{"given":"STANLEY","family":"BURRIS","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOHN","family":"LAWRENCE","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196791000249","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:36:40Z","timestamp":1565131000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196791000249"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[1991,9]]}},"alternative-id":["10.1142\/S0218196791000249"],"URL":"https:\/\/doi.org\/10.1142\/s0218196791000249","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}