{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:07:42Z","timestamp":1759032462625},"reference-count":25,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2009,5,15]],"date-time":"2009-05-15T00:00:00Z","timestamp":1242345600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Czech government, research program","award":["MSM6840770038"],"award-info":[{"award-number":["MSM6840770038"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper investigates a quasi\u2010variety of representable integral commutative residuated lattices axiomatized by the quasi\u2010identity resulting from the well\u2010known Wajsberg identity (<jats:italic>p<\/jats:italic> \u2192 <jats:italic>q<\/jats:italic>) \u2192 <jats:italic>q<\/jats:italic> \u2264 (<jats:italic>q<\/jats:italic> \u2192 <jats:italic>p<\/jats:italic>) \u2192 <jats:italic>p<\/jats:italic> if it is written as a quasi\u2010identity, i. e., (<jats:italic>p<\/jats:italic> \u2192 <jats:italic>q<\/jats:italic>) \u2192 <jats:italic>q<\/jats:italic> \u2248 <jats:bold>1<\/jats:bold> \u21d2 (<jats:italic>q<\/jats:italic> \u2192 <jats:italic>p<\/jats:italic>) \u2192 <jats:italic>p<\/jats:italic> \u2248 <jats:bold>1<\/jats:bold>. We prove that this quasi\u2010identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi\u2010variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL\u2010algebras, for instance we answer negatively H\u00e1jek's question asking whether the variety of \u03a0MTL\u2010algebras is generated by its Archimedean members (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710091","type":"journal-article","created":{"date-parts":[[2009,5,15]],"date-time":"2009-05-15T17:52:26Z","timestamp":1242409946000},"page":"320-336","source":"Crossref","is-referenced-by-count":2,"title":["Archimedean classes in integral commutative residuated chains"],"prefix":"10.1002","volume":"55","author":[{"given":"Rostislav","family":"Hor\u010d\u00edk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franco","family":"Montagna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2009,5,15]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00329-8"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-003-1822-4"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"W. J.Blok andD.Pigozzi Algebraizable Logics. 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