On L -fuzzy ideals in semirings. I

Young Bae Jun; Joseph Neggers; Hee Sik Kim

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 669-675
  • ISSN: 0011-4642

Abstract

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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 μ of R is characteristic iff μ is L -fuzzy characteristic.

How to cite

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Jun, Young Bae, Neggers, Joseph, and Kim, Hee Sik. "On $L$-fuzzy ideals in semirings. I." Czechoslovak Mathematical Journal 48.4 (1998): 669-675. <http://eudml.org/doc/30445>.

@article{Jun1998,
abstract = {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.},
author = {Jun, Young Bae, Neggers, Joseph, Kim, Hee Sik},
journal = {Czechoslovak Mathematical Journal},
keywords = {semiring; $L$-fuzzy (characteristic) ideal; level ideal; semirings; fuzzy ideals; level ideals},
language = {eng},
number = {4},
pages = {669-675},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $L$-fuzzy ideals in semirings. I},
url = {http://eudml.org/doc/30445},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Jun, Young Bae
AU - Neggers, Joseph
AU - Kim, Hee Sik
TI - On $L$-fuzzy ideals in semirings. I
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 669
EP - 675
AB - 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.
LA - eng
KW - semiring; $L$-fuzzy (characteristic) ideal; level ideal; semirings; fuzzy ideals; level ideals
UR - http://eudml.org/doc/30445
ER -

References

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  2. 10.1090/S0002-9939-1969-0237575-4, Proc. Amer. Math. Soc. 21 (1969), 412–416. (1969) Zbl0197.02902MR0237575DOI10.1090/S0002-9939-1969-0237575-4
  3. Direct sums of semirings and the Krull-Schmidt theorem, Kyungpook Math. J. 17, 135–141. Zbl0382.16019MR0463248
  4. On quotient semiring and extension of quotient halfring, Comm. Korean Math. Soc. 4 (1989), 17–22. (1989) 
  5. Fuzzy invariants subgroups and fuzzy ideals, Fuzzy Sets and Sys. 8 (1987), 133–139. (1987) MR0666626
  6. On fuzzy ideals of a ring I, Fuzzy Sets and Sys. 21 (1987), 99–104. (1987) MR0868358
  7. [unknown], Fuzzy prime idelas of rings J. Math. Anal. Appl. 134 (1988), 345–350. (1988) 
  8. Prime L-fuzzy ideals and primary L-fuzzy ideals, Fuzzy Sets and Sys. 27 (1988), 345–350. (1988) Zbl0663.13001MR0956381
  9. 10.1016/S0019-9958(65)90241-X, Inform. and Control 8 (1965), 338–353. (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X

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