Browse > Article
http://dx.doi.org/10.4134/CKMS.2008.23.1.001

ORDER SYSTEMS, IDEALS AND RIGHT FIXED MAPS OF SUBTRACTION ALGEBRAS  

Jun, Young-Bae (DEPARTMENT OF MATHEMATICS EDUCATION (AND RINS) GYEONGSANG NATIONAL UNIVERSITY)
Park, Chul-Hwan (DEPARTMENT OF MATHEMATICS UNIVERSITY OF ULSAN)
Roh, Eun-Hwan (DEPARTMENT OF MATHEMATICS EDUCATION CHINJU NATIONAL UNIVERSITY OF EDUCATION)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.1, 2008 , pp. 1-10 More about this Journal
Abstract
Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.
Keywords
(weak, complicated) subtraction algebra; (irreducible) ideal; order system; right fixed map; kernel;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ., Vol. 25, second edition 1984; third edition, 1967, Providence
2 G. Gratzer, Universal Algebra, 2nd edition, Springer-Verlag, New York Inc., 1979
3 J. C. Abbott, Semi-Boolean algebras, Matemat. Vesnik 4 (1967), 177-198
4 J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston 1969
5 Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. Online e-2006 (2006), 1081-1086
6 Y. B. Jun, H. S. Kim, and K. J. Lee, The essence of subtraction algebras, Sci. Math. Jpn. Online e-2006 (2006), 1069-1074
7 Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. Online e-2004 (2004), 397-402
8 S. S. Ahn, Y. H. Kim, and K. J. Lee, A relation on subtraction algebras, Sci. Math. Jpn. Online e-2005 (2005), 51-55
9 Y. B. Jun, Y. H. Kim, and K. J. Lee, Weak forms of subtraction algebras, Bull. Korean Math. Soc. (submitted)   과학기술학회마을   DOI   ScienceOn
10 Y. B. Jun, Y. H. Kim, and K. A. Oh, Subtraction algebras with additional conditions, Commun. Korean Math. Soc. (submitted).   과학기술학회마을   DOI   ScienceOn
11 Y. B. Jun and K. H. Kim, Prime and irreducible ideals in subtraction algebras, Ital. J. Pure Appl. Math. (submitted)
12 Y. B. Jun, X. L. Xin, and E. H. Roh, A class of algebras related to BCI-algebras and semigroups, Soochow J. Math. 24 (1998), no. 4, 309-321
13 B. M. Schein, Difference Semigroups, Comm. Algebra 20 (1992), 2153-2169   DOI   ScienceOn
14 B. Zelinka, Subtraction Semigroups, Math. Bohemica 120 (1995), 445-447
15 Y. H. Kim and H. S. Kim, Subtraction algebras and BCK-algebras, Math. Bohemica 128 (2003), no. 1, 21-24