Fuzzy $h$-ideal of Matrix Hemiring $S_{2}=left( begin{array}{cc} R & Gamma \ S & L \ end{array} right)$

Document Type: Research Paper

Authors

1 Department of Mathematics, Jadavpur University, Kolkata, India

2 Department of Mathematics, Yazd University, Yazd, Iran

Abstract

The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.

Keywords


bibitem{B} Y. Bingxue, {it Fuzzy semi-ideal and generalized fuzzy quotient ring}, Iranian Journal of Fuzzy Systems, {bf 5(2)} (2008), 87-92.


bibitem{D1} B. Davvaz and P. Corsini, {it On $(alpha,beta)$-fuzzy $Hsb v$-ideals of $Hsb v$-rings}, Iranian Journal of Fuzzy Systems, {bf5(2)} (2008), 35-47.

bibitem{D2} B. Davvaz, {it Fuzzy hyperideals in ternary semihyperrings}, Iranian Journal of Fuzzy Systems, {bf6(4)} (2009), 21-36.

bibitem{Dudek} W. A. Dudek, M. Shabir and R. Anjum, {it Characterization of hemirings by their $h$-ideals}, Computer Mathematics with Applications, {bf 59} (2010), 3167-3179.
bibitem{re:Dutta} T. K. Dutta and S. K. Sardar, {it On the operator semirings of a
$Gamma$-semiring}, Southeast Asian Bull.  Math.,
{bf 26} (2002), 203-213.

bibitem{Golan} J. S. Golan, {it Semirings and their applications}, Kluwer Academic
Publishers, 1999.

bibitem{Henriksen} M. Henriksen, {it Ideals in semirings with commutative addition},
Am. Math. Soc. Notices, {bf6} (1958), 321.

bibitem{Iizuka} K. Iizuka,{it  On the Jacobson radical of semiring}, Tohoku Math. J., {bf 11(2)}
(1959), 409-421.

bibitem{J} I. Jahan, {it Embedding of the lattice of ideals of a ring into its lattice of fuzzy ideals}, Iranian Journal of Fuzzy Systems, {bf 6(3)} (2009), 65-71.

bibitem{YBjun} Y. B. Jun,  M. A. "{O}zt"{u}rk and  S. Z. Song, {it On Fuzzy $h$-ideals in
hemiring}, Information Sciences, {bf 162} (2004), 211-226.

bibitem{LaTorre} D. R. La Torre, {it On $h$-ideals and $k$-ideals in hemirings}, Publ. Math. Debrecen,
{bf12} (1965), 219-226.

bibitem{Xma2} X. Ma and J. Zhan, {it Fuzzy $h$-ideals in $h$-hemiregular and $h$-simple $Gamma$-hemirings}, Neural Comput. Applic., {bf 19} (2010), 477-485.

bibitem{Rao} M. M. K. Rao, {it $Gamma-$semirings-1}, Southeast Asian Bull. of Math.,
{bf 19} (1995), 49-54.

bibitem{Saha} B. C. Saha and  S. K. Sardar, {it On semiring $left(
                                                                                           begin{array}{cc}
                                                                                             R & Gamma
                                                                                             S & L
                                                                                           end{array}
                                                                                         right)
$ and morita context}, Int. J. Alg., {bf4} (2010), 303-315.

bibitem{Saha2}S. K. Sardar and  B. C. Saha, {it On nobusawa gamma semirings}, Universitatea Din Bacaau Studii Si Cercetari Stiintifice, Seria: Mathematica, {bf 18} (2008), 283-306.

bibitem{Sardar} S. K. Sardar and  D. Mandal, {it Fuzzy $h$-ideals in $Gamma$-hemiring}, Int. J. Pure. Appl.
Math., {bf56} (2009), 439-450.

bibitem{corresponding} S. K. Sardar, D. Mandal and B. Davvaz, {it Fuzzy $h$-ideal in $Gamma$-hemiring and its operator hemirings}, submitted.

bibitem{Regularity} S. K. Sardar and  D. Mandal, {it On fuzzy $h$-ideals in h-regular $Gamma$-hemirings and h-duo $Gamma$-hemirings}, General Mathematics Notes, to appear.

bibitem{Yin} Y. Yin and H. Li, {it The characterization of $h$-hemiregular hemirings and $h$-intra-hemiregular hemirings}, Information Sciences, {bf178} (2008), 3451-3464.
bibitem{Yin2} Y. Yin, X. Huang, D. Xu and  F. Li, {it The characterization of $h$-semisimple hemirings}, Int. J. Fuzzy Systems, {bf 11} (2009), 116-122.
bibitem{Zhan} J. Zhan and  W. A. Dudek, {it Fuzzy $h$-ideals of hemirings},
Information sciences,  {bf 177} (2007), 876-886.

bibitem{Z} J. Zhan, Y. B. Jun and B. Davvaz, {it  On $(in,invee q)$-fuzzy ideals of BCI-algebras}, Iranian Journal of Fuzzy Systems, {bf 6(1)}  (2009), 81-94.