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Title: MV-algebras are categorically equivalent to a class of $\scr{DR}l\sb {1(i)}$-semigroups (English)
Author: Rachůnek, Jiří
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 123
Issue: 4
Year: 1998
Pages: 437-441
Summary lang: English
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Category: math
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Summary: In the paper it is proved that the category of \MV-algebras is equivalent to the category of bounded \DRl-semigroups satisfying the identity $1-(1-x)=x$. Consequently, by a result of D. Mundici, both categories are equivalent to the category of bounded commutative \BCK-algebras. (English)
Keyword: categorical equivalence
Keyword: bounded \BCK-algebra
Keyword: \MV-algebra
Keyword: \DRl-semigroup
MSC: 03G20
MSC: 06D30
MSC: 06D35
MSC: 06F05
MSC: 06F35
idZBL: Zbl 0934.06014
idMR: MR1667115
DOI: 10.21136/MB.1998.125964
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Date available: 2009-09-24T21:34:04Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/125964
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Reference: [9] D. Mundici: MV-algebras are categorically equivalent to bounded commutative BCK-algebras.Math. Japonica 31 (1986), 889-894. Zbl 0633.03066, MR 0870978
Reference: [10] J. Rachůnek: DRI-semigroups and MV-algebras.Czechoslovak Math. J. 123 (1998), 365-372. MR 1624268, 10.1023/A:1022801907138
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Reference: [12] S. Tanaka: On $\Lambda$-commutative algebras.Math. Sem. Notes Kobe 3 (1975), 59-64. Zbl 0324.02053, MR 0419222
Reference: [13] T. Traczyk: On the variety of bounded commutative BCK-algebras.Math. Japonica 24 (1979), 283-292. Zbl 0422.03038, MR 0550212
Reference: [14] H. Yutani: Quasi-commutative BCK-algebras and congruence relations.Math. Sem. Notes Kobe 5 (1977), 469-480. Zbl 0375.02053, MR 0498112
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