Geodesic
On $L$-fuzzy ideals in semirings. I
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 669-675 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03E72, 04A72, 16D25, 16Y60
Keywords: semiring; $L$-fuzzy (characteristic) ideal; level ideal 
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Jun, Young Bae; Neggers, J.; Kim, Hee Sik. On $L$-fuzzy ideals in semirings. I. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 669-675. http://geodesic.mathdoc.fr/item/CMJ_1998_48_4_a4/

[1] J. Ahsan and M. Shabir: Semirings with projective ideals. Math. Japonica 38 (1993), 271–276. | MR

[2] P. J. Allen: A fundamental theorem of homomorphisms for semirings. Proc. Amer. Math. Soc. 21 (1969), 412–416. | DOI | MR | Zbl

[3] L. Dale: Direct sums of semirings and the Krull-Schmidt theorem. Kyungpook Math. J. 17, 135–141. | MR | Zbl

[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

[6] T. K. Mukherjee and M. K. Sen: On fuzzy ideals of a ring I. Fuzzy Sets and Sys. 21 (1987), 99–104. | MR

[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 | Zbl

[9] L. A. Zadeh: Fuzzy sets. Inform. and Control 8 (1965), 338–353. | DOI | MR | Zbl