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On RM-algebras with an additional condition | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 27-38 اصل مقاله (460.47 K) | ||
| نوع مقاله: Special Issue Dedicated to Prof. Esfandiar Eslami | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.22243.1517 | ||
| نویسنده | ||
| Akbar Rezaei* | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| In this paper, we apply a new condition to RM-algebras. We obtain some relations among this condition with another axioms in some algebras of logic and some examples are given to illustrate them. %It is proved We prove that the relation derived from this new algebra is a partial ordering. It is proved that RM-algebras with condition (I) are abelian group. Also, we present that the BI-algebras, BCK-algebras, L-algebras, KL-algebras CL-algebras and BE-algebras satisfying (I) are trivial. | ||
| کلیدواژه‌ها | ||
| Groupoid؛ RM-algebra؛ BE-algebra؛ BI-algebra؛ L-algebra | ||
| مراجع | ||
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[1] Abbott, J. C. (1967). Semi-boolean algebras, Matematicki Vesnik, 4, 177{198.
[2] Borumand Saeid, A., Kim, H. S., & Rezaei, A. (2017). On BI-algebras, Analele Stiinti ceale Universitatii Ovidius Constanta, 25, 177{194.
[3] Chajda, I. (2006). Implication algebras, Discussiones Mathematicae General Algebra and Applications, 26, 141{153.
[4] Ciungu, L. C. (2021). Results in L-algebras, Algebra Universalis, 82:7. https://doi.org/10.1007/s00012-020-00695-1
[5] Imai, Y., & Iseki, K. (1966). On axiom system of propositional calculi, XIV. Proceedings of the Japan Academy, 42, 19{20.
[6] Iorgulescu, A. (2008). Algebras of logic as BCK-algebras, Bucharest University of Economics, Bucharest, Romania. [7] Iseki, K. (1966). An algebra related with a propositional calculus, Proceedings of the Japan Academy, 42, 26{29. [8] Hentzel, I. B., Jacobs, D. P., & Muddana, S. V. (1993). Experimenting with the Identity (xy)z = y(zx), Journal of Symbolic Computation, 16(3), 289{293. https://doi.org/10.1006/jsco.1993.1047
[9] Kim, H. S., & Neggers, J. (2008). The semigroups of binary systems and some perspectives, Bulletin of the Korean Mathematical Society, 45, 651{661.
[10] Kim, H. S., & Kim, Y. H. (2007). On BE-algebras, Scientiae Mathematicae Japonicae, 66, 113{117.
[11] Meng, B. L. (2010). CI-algebras, Scientiae Mathematicae Japonicae, 17, 11{17.
[12] Meng J. & Jun, Y. B. (1994). BCK-algebras, Kyung-Moon Sa Co. Seoul, Korea.
[13] Rump, W. (2008). L-algebras, self-similarity, and `-groups, Journal of Algebra, 320, 2328{2348.
[14] Rezaei, A., & Borumand Saeid, A. (2022). A new extension of RM-algebras, Asian-European Journal of Mathematics, 2250073. doi: 10.1142/S1793557122500735
[15] Smarandache, F., Rezaei, A., & Kim, H. S. (2020). A New trend to extensions of CI-algebras, International Journal of Neutrosophic Scienc, 15(1), 8{15.
[16] Walendziak, A. (2022). On implicative BE-algebras, Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, LXXVI(2), 45{54. doi: 0.17951/a.2022.76.2.45-54
[17] Walendziak, A. (2021). RM-algebras and commutative moons, International Electronic Journal of Algebra, 29, 95{106. https://doi.org/10.24330/ieja.852024
[18] Walendziak, A. (2019). The property of commutativity for some generalizations of BCK-algebras, Soft Computing, 23(17), 7505{7511. https://doi.org/10.1007/s00500-018-3691-y
[19] Walendziak, A. (2018). Deductive systems and congruences in RM-algebras, Journal of Multiple Valued Logic & Soft Computing, 30(4), 521{539.
[20] Walendziak, A. (2018). The implicative property for some generalizations of BCK-algebras, Journal of Multiple Valued Logic & Soft Computing, 31, 591{611. | ||
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