"303987" . . "2"^^ . . . . . "1"^^ . "Archimedean Classes in Integral Commutative Residuated Chains"@en . . "Z(MSM6840770038)" . "Archimedean Classes in Integral Commutative Residuated Chains" . "NORM BASED LOGIC; FUZZY LOGICS; LATTICES; ALGEBRAS; PROOF"@en . "3" . . . . . "This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety 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-algebras, for instance we answer negatively H\u00E1jek's question asking whether the variety of MTL-algebras is generated by its Archimedean members" . "[DBB1BE487D26]" . . "RIV/68407700:21230/09:00159057" . . . "Archimedean Classes in Integral Commutative Residuated Chains"@en . . "Archimedean Classes in Integral Commutative Residuated Chains" . "Mathematical Logic Quarterly" . "21230" . . "000267096600010" . "RIV/68407700:21230/09:00159057!RIV10-MSM-21230___" . . "This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety 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-algebras, for instance we answer negatively H\u00E1jek's question asking whether the variety of MTL-algebras is generated by its Archimedean members"@en . . "17"^^ . "55" . "Hor\u010D\u00EDk, Rostislav" . "DE - Spolkov\u00E1 republika N\u011Bmecko" . "0942-5616" .