IJPAM: Volume 54, No. 3 (2009)

PRE-PRIME AND PRE-SEMIPRIME IDEALS IN $\Gamma$-SEMIRINGS

Sujit Kumar Sardar$^1$, Bibhas Chandra Saha$^2$Chandidas Mahavidyalaya, Vill P.O.: Khujutipara, District: Birbhum, PIN: 731215, West Bengal, INDIA
$^{1,2}$Department of Mathematics
Faculty of Science
Jadavpur University
Kolkata, 700032, INDIA
$^1$e-mails: [email protected], [email protected]
$^2$e-mail: [email protected]


Abstract.The concepts of the pre-prime ideals and pre-semiprime ideals in $\Gamma$-semirings are introduced and some of their properties are studied here. Also the notions of pre-Noetherian and $k$-regular semiring ($\Gamma$-semiring) are introduced here.

Received: February 11, 2009

AMS Subject Classification: 16Y60, 16Y99, 20N10

Key Words and Phrases: pre-prime ideal, pre-semiprime ideal, $k$-regular semiring and $\Gamma$-semiring, operator semiring, pre-Noetherian semiring and $\Gamma$-semiring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3