Dedekind Complete Commutative BCK-algebras |
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| Authors: | Dvurečenskij Anatolij Graziano Maria Gabriella |
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| Affiliation: | (1) Mathematical Institute, Slovak Academy of Sciences, !["Scaron"]("/content/hn23553821r10415/xlarge352.gif") tefánikova 49, SK-814 73 Bratislava, Slovakia;(2) Dipartimento di Matematica e Applicazioni !["ldquo"]("/content/hn23553821r10415/xlarge8220.gif") R. Caccioppoli!["rdquo"]("/content/hn23553821r10415/xlarge8221.gif") , Università degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-801 26 Napoli, Italia |
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| Abstract: | We study Dedekind complete commutative BCK-algebras with the relative cancellation property and their connection with corresponding universal groups. We shall characterize Dedekind orthogonally complete atomic and Archimedean BCK-algebras, generalizing results of Jakubík known for MV-algebras. Finally, we characterize those Dedekind complete and atomic commutative BCK-algebras that are isomorphic to direct products of basic BCK-chains, generalizing a result of Cignoli for MV-algebras. |
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| Keywords: | atomic BCK-algebra commutative BCK-algebra Dedekind complete BCK-algebra relative cancellation property subdirect product universal group |
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