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Ordered BCI-algebras, Y-kernels and (ordered) functions | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 1-13 اصل مقاله (161.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26608.1626 | ||
| نویسندگان | ||
| E. Yang* 1؛ E. H. Roh2؛ Y. B. Jun3 | ||
| 1Department of Philosophy, Jeonbuk National University, Jeonju 54896, Korea | ||
| 2Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Korea | ||
| 3Department of Mathematics Education Gyeongsang National University Jinju 52828, Korea | ||
| چکیده | ||
| The concept of kernels in ordered BCI-algebras was first introduced by Yang-Roh-Jun. This paper extends the concept to specific kernels, called here Y-kernels. To be more precise, two sorts of Y-kernels related to function were first introduced and the relations between them and between these Y-kernels and kernels were studied. Next, related to ordered function (and (ordered) homomorphism) the same relations are investigated. | ||
| کلیدواژهها | ||
| Kernel؛ Y-kernel؛ Ordered BCI-algebra؛ Ordered function | ||
| مراجع | ||
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[1] K. Bimbó and J. M. Dunn, Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi, CSLI Publications, Stanford, 2008. [2] P. Cintula,Weakly implicative (fuzzy) logics I: basic properties, Arch. Math. Log., 45 (2006), 673–704. [3] P. Cintula and C. Noguera, Implicational (semilinear) logics I: a new hierarchy, Arch. Math. Log., 49 (2010), 417–446. [4] P. Cintula and C. Noguera, A general framework for mathematical fuzzy logic, P. Cintula, P. Hájek and C. Noguera (eds.) Handbook of Mathematical Fuzzy Logic, vol. 1, College Publications, London, (2011), 103-–207. [5] P. Cintula and C. Noguera, Implicational (semilinear) logics III: completeness properties, Arch. Math. Log., 57 (2018), 391–420. [6] J. M. Dunn, Partial gaggles applied to logics with restricted structural rules, P. Schroeder- Heister and K. Doˇsen, (eds.) Substructural Logics, Clarendon, Oxford, (1993), 63–108. [7] J. M. Dunn and G. Hardegree, Algebraic Methods in Philosophical Logic, Oxford Univ Press, Oxford, 2001. [8] R. Jansana and T. Moraschini, Relational semantics, ordered algebras, and quantifiers for deductive systems, manuscript, 2018. [9] J. G. Raftery, Order algebraizable logics, Ann. Pure Appl. Logic, 164 (2013), 251–283. [10] E. Yang and J. M. Dunn, Implicational tonoid logics: algebraic and relational semantics, Log. Univers., 15 (2021), 435–456. [11] E. Yang and J. M. Dunn, Implicational Partial Galois Logics: Relational semantics, Log. Univers., 15 (2021), 457–476. [12] E. Yang, E. H. Roh and Y. B. Jun, An introduction to the theory of OBCI-algebras, AIMS Math., 9 (2024), 36336-36350. [13] E. Yang, E. H. Roh and Y. B. Jun, Ordered homomorphisms and kernels of ordered BCIalgebras, Kexue Tongbao/CSB, 69 (2025), 04. [14] E. Yang, E. H. Roh and Y. B. Jun, Ordered maps and kernels of ordered BCI-algebras, J. Algebra Relat. Top., (1) 13 (2025), 135-157. | ||
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