On Prime and Maximal k-Subsemimodules of Semimodules

Abstract

In this paper, we present some characterizations of prime k-ideals and
maximal k-ideals of a semiring. Then we extend these properties to
prime k-subsemimodules and maximal k-subsemimodules of a semimodule. After that, the correspondence between prime k-ideals and
prime k-subsemimodules, and between maximal k-ideals and maximal
k-subsemimodules are given.

Keywords

• Prime k-ideal,Maximal k-ideal,Prime k-subsemimodule,Maximal ksubsemimodule,2000 AMS Classification: 16 Y 60

References

1. Allen, P. J. A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21, 412–416, 1969.
2. Allen, P. J. Neggers, J. and Kim, H. S. Ideal theory in commutative A-semirings, Kyungpook Math. J. 46, 261–271, 2006.
3. Iseki, K. Ideal theory of semirings, Proceedings Japan Academy 32, 554–559, 1956.
4. LaTorre, D. R. A note on quotient semirings, Proc. Amer. Math. Soc. 24, 463–465, 1970.
5. Chin-Pi Lu, C.-P. Unions of prime submodules, Houston J. Math. 23 (2), 203–213, 1997.
6. Sen, M. K. and Adhikari, M. R. On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118(3), 699–703, 1993.
7. Shabir, M. and Iqbal, M. S. One-sided prime ideals in semirings, Kyungpook Math. J. 47, 473–480, 2007.
8. Weinert, H. J., Sen, M. K. and Adhikari, M. R. One-sided k-ideals and h-ideals in semirings, Math. Pannon. 7 (1), 147–162, 1996.