Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GENERALIZED IDEAL ELEMENTS IN le-Γ-SEMIGROUPS

  • Hila, Kostaq (Department of Mathematics and Computer Science University of Gjirokastra) ;
  • Pisha, Edmond (Department of Mathematics Faculty of Natural Sciences University of Tirana)
  • Received : 2010.02.17
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we introduce and give some characterizations of (m, n)-regular le-${\Gamma}$-semigroup in terms of (m, n)-ideal elements and (m, n)-quasi-ideal elements. Also, we give some characterizations of subidempotent (m, n)-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

Keywords

References

  1. K. Hila, Characterizations on regular $le-{\Gamma}-semigroups$, Math. Sci. Res. J. 10 (2006), no. 5, 121-130.
  2. K. Hila, Some elements and Green's relation H in $le-{\Gamma}-semigroups$, Far East J. Math. Sci. (FJMS) 21 (2006), no. 2, 153-161.
  3. K. Hila, Filters in ordered ${\Gamma}-semigroups$, Rocky Mountain J. Math. 41 (2011), no. 1, 189-203. https://doi.org/10.1216/RMJ-2011-41-1-189
  4. K. Hila, On quasi-prime, weakly quasi-prime left ideals in ordered ${\Gamma}-semigroups$, Math. Slovaca 60 (2010), no. 2, 195-212. https://doi.org/10.2478/s12175-010-0006-x
  5. K. Hila, On some classes of $le-{\Gamma}-semigroups$, Algebras Groups Geom. 24 (2007), no. 4, 485-496.
  6. K. Hila and E. Pisha, On lattice-ordered Rees matrix ${\Gamma}-semigroups$, An. Stiint. Univ. Al. I. Cuza Iasi, Mat., accepted, to appear.
  7. K. Iseki, On (m, n)-antiideals in semigroup, Proc. Japan Acad. 38 (1962), 316-317. https://doi.org/10.3792/pja/1195523340
  8. N. Kehayopulu, On (m, n)-regular le-semigroups, Math. Balkanica 5 (1975), no. 27, 152-154.
  9. N. Kehayopulu, Generalized ideal elements in poe-semigroups, Semigroup Forum 25 (1982), no. 3-4, 213-222. https://doi.org/10.1007/BF02573600
  10. D. Krgovic, On (m, n)-regular semigroups, Publ. Inst. Math. (Beograd) (N.S.) 18(32) (1975), 107-110.
  11. D. N. Krgovic and S. Lajos, Notes on semigroups II, Karl Marx Univ. Econ., Dept. Math., Budapest 1976.
  12. Y. I. Kwon On minimal quasi-ideal elements in $poe-{\Gamma}-semigroups$, Far East J. Math. Sci (FJMS) 14 (2004), no. 3, 385-392.
  13. Y. I. Kwon and S. K. Lee, Some special elements in ordered ${\Gamma}-semigroups$, Kyungpook Math. J. 35 (1996), no. 3, 679-685.
  14. S. Lajos, On generalized ideals in semigroups (In Hungarian), Matematikai Lapok 10 (351) (1959).
  15. S. Lajos, Generalized ideals in semigroups, Acta Sci. Math. Szeged 22 (1961), 217-222.
  16. S. Lajos, Notes on (m, n)-ideals I, Proc. Japan Acad. 39 (1963), 419-421. https://doi.org/10.3792/pja/1195522988
  17. S. Lajos, Notes on (m, n)-ideals II, Proc. Japan Acad. 40 (1964), 631-632. https://doi.org/10.3792/pja/1195522640
  18. S. Lajos, On (m, n)-ideals of semigroups, Second Hungarian Math. Congress, vol. I (1960), 42-44.
  19. M. K. Sen, On ${\Gamma}-semigroups$, Algebra and its applications (New Delhi, 1981), 301-308, Lecture Notes in Pure and Appl. Math., 91, Dekker, New York, 1984.
  20. M. K. Sen and N. K. Saha, On ${\Gamma}-semigroup$. I, Bull. Calcutta Math. Soc. 78 (1986), no. 3, 180-186.