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BY-NC-ND 3.0 license Open Access Published by De Gruyter November 15, 2014

BM-Algebras and related topics

Andrzej Walendziak
From the journal Mathematica Slovaca


Some connections between BM-algebras and its related topics are studied. It is proved that the class of medial BH-algebras coincides with the class of BM-algebras. Moreover, the congruence lattice of a BM-algebra is investigated.

[1] BANDARU, R. K.: On BRK-algebras, Int. J. Math. Math. Sci. 2012 (2012), Article ID 952654, 12 pp. Search in Google Scholar

[2] BIRKHOFF, G.: Lattice Theory (3rd ed.), Amer. Math. Soc., Providence, RI, 1967. Search in Google Scholar

[3] HU, Q, P.— LI, X.: On BCH-algebras, Math. Seminar Notes 11 (1983), 313–320. Search in Google Scholar

[4] IMAI, Y.— ISÉKI, K.: On axiom system of propositional calculi, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19–22. Search in Google Scholar

[5] ISÉKI, K.: An algebra related with a propositional calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26–29. Search in Google Scholar

[6] JUN, Y. B.— ROH, E. H.— KIM, H. S.: On BH-algebras, Sci. Math. Jpn. 1 (1998), 347–354. Search in Google Scholar

[7] KIM, Ch. B.— KIM, H. S.: On BG-algebras, Demonstratio Math. 41 (2008), 497–505. Search in Google Scholar

[8] KIM, Ch. B.— KIM, H. S.: On BM-algebras, Sci. Math. Jpn. 63 (2006), 421–427. Search in Google Scholar

[9] KIM, H. S.— KIM, Y. H.— NEGGERS, J.: Coxeter algebras and pre-Coxeter algebras in Smarandache setting, Honam Math. J. 26 (2004), 471–481. Search in Google Scholar

[10] KOMORI, Y.: The class of BCC-algebras is not a variety, Math. Japonica 29 (1984), 391–394. Search in Google Scholar

[11] LI, H. S.: An axiom system of BCI-algebras, Math. Japonica 30 (1985), 351–352. Search in Google Scholar

[12] MENG, J.— XIN, X. L.: Implicative BCI-algebras, Pure Appl. Math. 8 (1992), 99–103. Search in Google Scholar

[13] NEGGERS, J.— KIM, H. S.: On B-algebras, Mat. Vesnik 54 (2002), 21–29. Search in Google Scholar

[14] YE, R.: On BZ-algebras. In: Selected Papers on BCI, BCK-algebras and Computer Logics, Shaghai Jiaotong University, 1991, pp. 21–24. Search in Google Scholar

[15] WALENDZIAK, A.: On BF-algebras, Math. Slovaca 57 (2007), 119–128. in Google Scholar

Published Online: 2014-11-15
Published in Print: 2014-10-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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