caa a22 4500 605470561 CHVBK 20210128100328.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00500-014-1365-y doi (NATIONALLICENCE)springer-10.1007/s00500-014-1365-y On varieties of basic algebras [Elektronische Daten] [Ivan Chajda, Radomír Halaš] It is known that the variety of commutative basic algebras, the variety of MV-algebras, the variety of orthomodular lattices and hence also the variety of Boolean algebras are proper subvarieties of the variety of basic algebras. In the paper several possible axiomatizations of the variety of basic algebras are provided. The variety of symmetric basic algebras is introduced and shown to be a proper subvariety of the variety of commutative basic algebras, and whose members have the underlying lattices distributive. It is proved that commutative basic algebras can be described as residuated $$l$$ l -groupoids. Springer-Verlag Berlin Heidelberg, 2014 Basic algebra nationallicence Commutative basic algebra nationallicence Symmetric basic algebra nationallicence Defining identity nationallicence MV-algebra nationallicence Orthomodular lattice nationallicence Chajda Ivan Department of Algebra and Geometry, Faculty of Science, Palacký University, 17.listopadu12, 77146, Olomouc, Czech Republic aut Halaš Radomír Department of Algebra and Geometry, Faculty of Science, Palacký University, 17.listopadu12, 77146, Olomouc, Czech Republic aut Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 261-267 1432-7643 19:2<261 2015 19 500 https://doi.org/10.1007/s00500-014-1365-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1365-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chajda Ivan Department of Algebra and Geometry, Faculty of Science, Palacký University, 17.listopadu12, 77146, Olomouc, Czech Republic aut NATIONALLICENCE 700 1- Halaš Radomír Department of Algebra and Geometry, Faculty of Science, Palacký University, 17.listopadu12, 77146, Olomouc, Czech Republic aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 261-267 1432-7643 19:2<261 2015 19 500