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Pure submodules of BCK-modules | ||
| Journal of Hyperstructures | ||
| دوره 3، شماره 1، شهریور 2014، صفحه 10-17 اصل مقاله (265.32 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2014.2568 | ||
| نویسندگان | ||
| N. Motahari* 1؛ T. Roudbari Lor2 | ||
| 1Department of Mathematics, Sciences and Research University, Kerman Branch, Kerman, Iran | ||
| 2Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran | ||
| چکیده | ||
| In this paper by considering the notion of BCK-module, we introduce pure BCK- submodules and we prove some results by it. In particular, we show that if X is a BCK- algebra, M is a cyclic BCK-module and N a prime BCK- submodule of M, then N is a pure BCK-submodule of M. | ||
| کلیدواژه‌ها | ||
| BCK- algebra؛ BCK- module؛ multiplication BCK- module؛ prime BCKsubmodule؛ pure BCK- submodule | ||
| مراجع | ||
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[1] H .A .S. Abujabal, M. Aslam and A. B. Thaheem, On actions of BCK- algebras on groups, Panamerican Mathematical Journal, 4 (1994), 43–48. [2] H. A. S. Abujabal, M. A. obaid and A. B. Thaheem, On annihilators of BCK-algebras , Czechoslovak Mathematical Journal, 45 (1995) 727-735. [3] M. Bakhshi, M. M. Zahedi and R. A. Borzooei, Fuzzy (positive, weak implicative) Hyper BCK-ideal. Iranian Journal of fuzzy system , 1 (2004), 63–79. [4] R. A. Borzooei, J. Shohani and M. Jafari, Extended BCK-module, World Applied Sciences Journal, 14 (2011), 1843–1850. [5] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV, Proc. Japan Academy, 42 (1996), 19–22. [6] B. Imran and M. Aslam, On certain BCK-modules, Southest Asian Bulletin of Mathematics, 34 (2010), 1–10. [7] A. Iorgulescu, Algebras of logic as BCK-algebras, Bucharest: Editura ASE (2008). [8] K. Iseki, An algebraic related with a propositional calculus, Proc. Japan Acad,42 (1966), 26–29. [9] J. Meng and Y. B. Jun, BCK-algebras, Korea: Kyungmoon Sa Co (1994). [10] N. Motahari nad T. Roudbari, Topics on multiplication BCK-modules, Proceed-ing of the 22th Algebra seminar, Tarbiat Moallem University, Sabzevar,Iran, [11] N. Motahari and T. Roudbari, Prime BCK-sub modules of BCK-modules, to appear in AUA Journal, [12] Z. Perveen, M. Aslam and A. B. Thaheem, On BCK- modules,Southeast Asian Bulletin of Mathematics,30(2006),317–329. | ||
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