Characterizations of hemirings by their h-ideals

Computers and Mathematics with Applications

Volumn 59, Issue 9, 2010, Pages 3167-3179

  Dudek, Wieslaw A ^a   Shabir, Muhammad ^b   Anjum, Rukhshanda ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

Fuzzy irreducible h ideal; Fuzzy prime h ideal; Irreducible h ideal; Prime h ideal

Indexed keywords

LEVEL SET;

EID: 77950864910     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.03.003     Document Type: Article

References (30)

1. Vandiver H.S. Note on a simple type of algebra in which cancellation law of addition does not hold. Bull. Amer. Math. Soc. 40 (1934) 914-920
2. Aho A.W., and Ullman J.D. Introduction to Automata Theory, Languages and Computation (1976), Addison Wesley, Reading, MA
3. Conway J.H. Regular Algebra and finite Machines (1971), Chapman and Hall, London
4. Eilenberg S. Automata, Languages and Machines (1974), Acedmic press, New York
5. Hebisch U., and Weinert H.J. Semirings: Algebraic Theory and Applications in the Computer Science (1998), World Scientific
6. Kuich W., and Salomma A. Semirings, Automata, Languages (1986), Springer Verlag, Berlin
7. Benson D.B. Bialgebras: some foundations for distributed and concurrent computation. Fund. Inform. 12 (1989) 427-486
8. Golan J.S. Semirings and their Applications (1999), Kluwer Acad. Publ.
9. Glazek K. A Guide to Literature on Semirings and their Applications in Mathematics and Information Sciences with Complete Bibliography (2002), Kluwer Acad. Publ., Dodrecht
10. Lee E.T., and Zadeh L.A. Note on fuzzy languages. Inform. Sci. 1 (1969) 421-434
11. Negoita C.V., and Ralescu D.A. Applications of Fuzzy Sets to System Analysis (1975), Birkhauser, Basel
12. Wee W.G., and Fu K.S. A formulation of fuzzy automata and its applications as a model of learning system. IEEE Trans. Syst. Sci. Cybern. SSC-5 (1969) 215-233
13. Henriksen M. Ideals in semirings with commutative addition. Amer. Math. Soc. Notices 6 (1958) 321
14. Iizuka K. On the Jacobson radial of a semiring. Tohoku Math. J. 11 (1959) 409-421
15. Ahsan J., Saifullah K., and Farid Khan M. Fuzzy semirings. Fuzzy Sets Systems 60 (1993) 309-320
16. Jun Y.B., Öztürk M.A., and Song S.Z. On fuzzy h-ideals in hemiring. Inform. Sci. 162 (2004) 211-226
17. Zhan J. On properties of fuzzy left h-ideals in hemirings. Int. J. Math. Math. Sci. 19 (2005) 3127-3144
18. Zhan J., and Dudek W.A. Fuzzy h-ideals of hemirings. Inform. Sci. 177 (2007) 876-886
19. Zadeh L.A. Fuzzy sets. Inf. Control 8 (1965) 338-353
20. Ahsan J. Semirings characterized by their fuzzy ideals. J. Fuzzy Math. 6 (1998) 181-192
21. Ghosh S. Fuzzy k-ideals of semirings. Fuzzy Sets Systems 95 (1998) 103-108
22. Kim C.B., and Park M. k-fuzzy ideals in semirings. Fuzzy Sets Systems 81 (1996) 281-286
23. Akram M., and Dudek W.A. Intuitionistic fuzzy left k-ideals of semirings. Soft Comput. 12 (2008) 881-890
24. Dudek W.A. Special types of intuitionistic fuzzy left h-ideals of hemirings. Soft Comput. 12 (2008) 359-364
25. LaTorre D.R. On h-ideals and k-ideals in hemirings. Publ. Math. (Debrecen) 12 (1965) 219-226
26. Ma X., and Zhan J. On fuzzy h-ideals of hemirings. J. Syst. Sci. Complexity 20 (2007) 470-478
27. Ma X., and Zhan J. Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings. Inform. Sci. 179 (2009) 1249-1268
28. Kondo M., and Dudek W.A. On the Transfer Principle in fuzzy theory. Mathware Soft Comput. 12 (2005) 41-55
29. Yin Y., and Li H. The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings. Inform. Sci. 178 (2008) 3451-3464
30. Birkhoff G. Lattice Theory (1954), Amer. Math. Soc. Colleq. Publications