h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R & \Gamma\\S & L\end{array}\right)$

Kumar Sardar Sujit; Chandra Saha Bibhas

$h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R & \Gamma\\S & L\end{array}\right)$$

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Title: h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R & \Gamma\\S & L\end{array}\right)$

Volume:

Number:

ISSN:

1829-1163

Official URL:

Contributor(s):

Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան

Coverage:

105-119

Abstract:

n this paper we show that h-prime and h-semiprime ideals in a Nobusawa $\Gamma$-semiring are preserved by the functions $^{*'}(~)$, $^{+'}(~)$, $^{*}(~)$, $^{+}(~)$, $\Gamma (~)$ and S( ). This preservation property is then used to characterize h-prime and h-semiprime ideals in matrix semiring $\left(\begin{array}{ll} R & \Gamma \\ S & L \end{array} \right)$. Moreover, characterization theorems of h-regular and H-Noetherian $\Gamma-$semirings have been obtained.