| Title:
|
On $L$-fuzzy ideals in semirings. I (English) |
| Author:
|
Jun, Young Bae |
| Author:
|
Neggers, J. |
| Author:
|
Kim, Hee Sik |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
669-675 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
semiring |
| Keyword:
|
$L$-fuzzy (characteristic) ideal |
| Keyword:
|
level ideal |
| MSC:
|
03E72 |
| MSC:
|
04A72 |
| MSC:
|
16D25 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 0954.16032 |
| idMR:
|
MR1658233 |
| . |
| Date available:
|
2009-09-24T10:17:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127445 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/127473 |
| . |
| Reference:
|
[1] J. Ahsan and M. Shabir: Semirings with projective ideals.Math. Japonica 38 (1993), 271–276. MR 1213388 |
| Reference:
|
[2] P. J. Allen: A fundamental theorem of homomorphisms for semirings.Proc. Amer. Math. Soc. 21 (1969), 412–416. Zbl 0197.02902, MR 0237575, 10.1090/S0002-9939-1969-0237575-4 |
| Reference:
|
[3] L. Dale: Direct sums of semirings and the Krull-Schmidt theorem.Kyungpook Math. J. 17, 135–141. Zbl 0382.16019, MR 0463248 |
| Reference:
|
[4] H. S. Kim: On quotient semiring and extension of quotient halfring.Comm. Korean Math. Soc. 4 (1989), 17–22. |
| Reference:
|
[5] Wang-jin Liu: Fuzzy invariants subgroups and fuzzy ideals.Fuzzy Sets and Sys. 8 (1987), 133–139. MR 0666626 |
| Reference:
|
[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 |
| Reference:
|
[7] K. L. N. Swamy and U. M. Swamy: .Fuzzy prime idelas of rings J. Math. Anal. Appl. 134 (1988), 345–350. |
| Reference:
|
[8] Zhang Yue: Prime L-fuzzy ideals and primary L-fuzzy ideals.Fuzzy Sets and Sys. 27 (1988), 345–350. Zbl 0663.13001, MR 0956381 |
| Reference:
|
[9] L. A. Zadeh: Fuzzy sets.Inform. and Control 8 (1965), 338–353. Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
| . |
