TY - JOUR T1 - On Prime and Maximal k-Subsemimodules of Semimodules AU - Yeşilot, Gürsel PY - 2010 DA - March JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 305 EP - 312 VL - 39 IS - 3 LA - en AB - In this paper, we present some characterizations of prime k-ideals andmaximal k-ideals of a semiring. Then we extend these properties toprime k-subsemimodules and maximal k-subsemimodules of a semimodule. After that, the correspondence between prime k-ideals andprime k-subsemimodules, and between maximal k-ideals and maximalk-subsemimodules are given. KW - Prime k-ideal KW - Maximal k-ideal KW - Prime k-subsemimodule KW - Maximal ksubsemimodule KW - 2000 AMS Classification: 16 Y 60 CR - Allen, P. J. A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21, 412–416, 1969. CR - Allen, P. J. Neggers, J. and Kim, H. S. Ideal theory in commutative A-semirings, Kyungpook Math. J. 46, 261–271, 2006. CR - Iseki, K. Ideal theory of semirings, Proceedings Japan Academy 32, 554–559, 1956. CR - LaTorre, D. R. A note on quotient semirings, Proc. Amer. Math. Soc. 24, 463–465, 1970. CR - Chin-Pi Lu, C.-P. Unions of prime submodules, Houston J. Math. 23 (2), 203–213, 1997. CR - Sen, M. K. and Adhikari, M. R. On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118(3), 699–703, 1993. CR - Shabir, M. and Iqbal, M. S. One-sided prime ideals in semirings, Kyungpook Math. J. 47, 473–480, 2007. CR - 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. UR - https://dergipark.org.tr/en/pub/hujms/article/101491 L1 - https://dergipark.org.tr/en/download/article-file/86691 ER -