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On \(d\)-algebras. (English) Zbl 0943.06012
There exist various generalizations of BCK-algebras. \(d\)-algebras are one of them. In this paper, the notion of a \(d\)-algebra is introduced and several relations between \(d\)-algebras and BCK-algebras are investigated. It is shown that the class of oriented digraphs corresponds in a simple way to the class of edge \(d\)-algebras and that arbitrary \(d\)-algebras also determine unique edge \(d\)-algebras in a natural manner.

MSC:
06F35 BCK-algebras, BCI-algebras
05C20 Directed graphs (digraphs), tournaments
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References:
[1] HU, QING PING-LI, XIN: On BCH-algebras. Math. Semin. Notes, Kobe Univ. 11 (1983), 313-320. · Zbl 0579.03047
[2] HU, QING PING-LI, XIN: On proper BCH-algebras. Math. Japon. 30 (1985), 659-661. · Zbl 0583.03050
[3] ISÉKI K.-TANAKA S.: An introduction to theory of BCK-algebras. Math. Japon. 23 (1978), 1-26.
[4] ISÉKI K.: On BCI-algebras. Math. Semin. Notes, Kobe Univ. 8 (1980), 125-130. · Zbl 0473.03059
[5] MENG J.: Implicative commutative semigroups are equivalent to a class of BCK -algebras. Semigroup Forum 50 (1995), 89-96. · Zbl 0807.06011
[6] MUNDICI D.: MV-algebras are categorically equivalent to bounded commutative BCK-algebras. Math. Japon. 31 (1986), 889-894. · Zbl 0633.03066
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