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On \(d\)-ideals in \(d\)-algebras. (English) Zbl 0960.06010
Motivated by the theory of BCK-algebras, the authors introduce the notions of \(d\)-subalgebras and \(d\)-ideals on \(d\)-algebras. A \(d\)-algebra is an algebra \((X;\ast ,0)\) of type \((2,0)\) such that (i) \(x \ast x = 0\), (ii) \(0 \ast x = 0\), and (iii) \(x \ast y = 0\) and \(y \ast x = 0\) imply \(x = y.\) The idea of a quotient \(d\)-algebra is introduced, some fundamental theorems of \(d\)-morphisms for \(d\)-algebras are presented, and some relationships among different types of \(d\)-ideals are given.

MSC:
06F35 BCK-algebras, BCI-algebras
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References:
[1] HU Q. P.-LI X.: On BCH-algebras. Math. Sem. Notes, Kobe Univ. 11 (1983), 313-320. · Zbl 0579.03047
[2] HU Q. P.-LI X.: On proper BCH-algebras. Math. Japon. 30 (1985), 659-661. · Zbl 0583.03050
[3] IMAI Y.-ISEKI K.: On axiom systems of propositional calculi XIV. Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19-22. · Zbl 0156.24812
[4] ISÉKI K.: An algebra related with a propositional calculus. Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26-29. · Zbl 0207.29304
[5] ISÉKI K.: On BCI-algebras. Math. Sem. Notes, Kobe Univ. 8 (1980), 125-130. · Zbl 0473.03059
[6] ISÉKI K.-TANAKA S.: Ideal theory of BCK-algebras. Math. Japon. 21 (1976), 351-366. · Zbl 0355.02041
[7] ISÉKI K.-TANAKA S.: An introduction to the theory of BCK-algebras. Math. Japon. 23 (1978), 1-26. · Zbl 0385.03051
[8] NEGGERS J.-KIM H. S.: On d-algebras. Math. Slovaca 49 (1999), 19-26. · Zbl 0943.06012
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