The notions of superior subalgebras and (commutative) superior ideals are introduced, and their relations and related properties are investigated. Conditions for a superior ideal to be commutative are provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1245, author = {Young Bae Jun and Seok Zun Song}, title = {Superior subalgebras and ideals of BCK/BCI-algebras}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {36}, year = {2016}, pages = {85-99}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1245} }
Young Bae Jun; Seok Zun Song. Superior subalgebras and ideals of BCK/BCI-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 36 (2016) pp. 85-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1245/
[000] [1] J. D. Bashford and P. D. Jarvis, The genetic code as a peridic table: algebraic aspects, BioSystems 57 (2000), 147-161. doi: 10.1016/S0303-2647(00)00097-6
[001] [2] L. Frappat, A. Sciarrino and P. Sorba, Crystalizing the genetic code, J. Biological Physics 27 (2001), 1-34. doi: 10.1023/A:1011874407742 | Zbl 1001.92009
[002] [3] Y. Huang, BCI-algebra (Science Press, Beijing, 2006). ISBN 97-7-03-015411.
[003] [4] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japonica 23 (1978), 1-26. | Zbl 0385.03051
[004] [5] Y.B. Jun and S.Z. Song, Codes based on BCK-algebras, Inform. Sci. 181 (2011), 5102-5109. doi: 10.1016/j.ins.2011.07.006 | Zbl 1241.94039
[005] [6] M.K. Kinyon and A.A. Sagle, Quadratic dynamical systems and algebras, J. Diff. Equ. 117 (1995), 67-126. doi: 10.1006/jdeq.1995.1049 | Zbl 0830.17001
[006] [7] J. Meng, Commutative ideals in BCK-algebras, Pure Appl. Math. (in China) 9 (1991), 49-53. | Zbl 0875.06017
[007] [8] J. Meng, On ideals in BCK-algebras, Math. Japonica 40 (1994), 143-154. | Zbl 0807.06012
[008] [9] J. Meng and Y.B. Jun, BCK-algebras (Kyungmoon Sa Co. Seoul, 1994).
[009] [10] R. Sáanchez, R. Grau and E. Morgado, A novel Lie algebra of the genetic code over the Galois field of four DNA bases, Mathematical Biosciences 202 (2006), 156-174. doi: 10.1016/j.mbs.2006.03.017 | Zbl 1100.92021
[010] [11] J.J. Tian and B.L. Li, Coalgebraic structure of genetics inheritance, Mathematical Biosciences and Engineering 1 (2004), PMID: 20369970 [PubMed], 243-266. | Zbl 1061.17027