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- W2529813863 abstract "ABSTRACTLoday introduced the notion of a dimonoid and constructed the free dimonoid. The paper concerns the variety theory of dimonoids. We recall and summarize the results obtained by Loday, the author as well as others on the structure of some relatively free dimonoids. This part of the paper should be viewed as a survey, however we include some new ideas in the last sections. Namely, we construct a free (lz;rs)-dimonoid, a free (rs;rz)-dimonoid, a free rs-dimonoid, a free (rb;rs)-dimonoid, a free (rs;rb)-dimonoid and characterize the least (lz;rs)-congruence, the least (rs;rz)-congruence, the least rs-congruence, the least (rb;rs)-congruence and the least (rs;rb)-congruence on the free dimonoid. We also establish that the automorphism groups of constructed free algebras are isomorphic to the symmetric group and the semigroups of the free rs-dimonoid are anti-isomorphic." @default.
- W2529813863 created "2016-10-14" @default.
- W2529813863 creator A5075305118 @default.
- W2529813863 date "2016-10-07" @default.
- W2529813863 modified "2023-09-26" @default.
- W2529813863 title "Structure of relatively free dimonoids" @default.
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- W2529813863 doi "https://doi.org/10.1080/00927872.2016.1222404" @default.
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