# Article

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Keywords:
semiring; $L$-fuzzy (characteristic) ideal; level ideal
Summary:
In this paper we extend the concept of an $L$-fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring $R$, and we show that each level left (resp. right) ideal of an $L$-fuzzy left (resp. right) ideal $\mu$ of $R$ is characteristic iff $\mu$ is $L$-fuzzy characteristic.
References:
[1] J. Ahsan and M. Shabir: Semirings with projective ideals. Math. Japonica 38 (1993), 271–276. MR 1213388
[2] P. J. Allen: A fundamental theorem of homomorphisms for semirings. Proc. Amer. Math. Soc. 21 (1969), 412–416. DOI 10.1090/S0002-9939-1969-0237575-4 | MR 0237575 | Zbl 0197.02902
[3] L. Dale: Direct sums of semirings and the Krull-Schmidt theorem. Kyungpook Math. J. 17, 135–141. MR 0463248 | Zbl 0382.16019
[4] H. S. Kim: On quotient semiring and extension of quotient halfring. Comm. Korean Math. Soc. 4 (1989), 17–22.
[5] Wang-jin Liu: Fuzzy invariants subgroups and fuzzy ideals. Fuzzy Sets and Sys. 8 (1987), 133–139. MR 0666626
[6] T. K. Mukherjee and M. K. Sen: On fuzzy ideals of a ring I. Fuzzy Sets and Sys. 21 (1987), 99–104. MR 0868358
[7] K. L. N. Swamy and U. M. Swamy: Fuzzy prime idelas of rings J. Math. Anal. Appl. 134 (1988), 345–350.
[8] Zhang Yue: Prime L-fuzzy ideals and primary L-fuzzy ideals. Fuzzy Sets and Sys. 27 (1988), 345–350. MR 0956381 | Zbl 0663.13001
[9] L. A. Zadeh: Fuzzy sets. Inform. and Control 8 (1965), 338–353. DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606

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