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

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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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 sem...

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Main Authors: Kumar Sardar Sujit, Chandra Saha Bibhas
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2009-10-01
Series:Armenian Journal of Mathematics
Online Access:http://www.armjmath.sci.am/index.php/ajm/article/view/58
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spelling doaj-4c2919d58e36410083d8a451761306182020-11-24T21:44:40ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632009-10-0123h-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 Sujit0Chandra Saha Bibhas1Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India.Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India. 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. http://www.armjmath.sci.am/index.php/ajm/article/view/58
collection DOAJ
language English
format Article
sources DOAJ
author Kumar Sardar Sujit
Chandra Saha Bibhas
spellingShingle Kumar Sardar Sujit
Chandra Saha Bibhas
h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
Armenian Journal of Mathematics
author_facet Kumar Sardar Sujit
Chandra Saha Bibhas
author_sort Kumar Sardar Sujit
title h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
title_short h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
title_full h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
title_fullStr h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
title_full_unstemmed h-prime and h-semiprime ideals in $\Gamma_{N}$-semirings and Matrix Semiring $\left(\begin{array}{ll}R&\Gamma\\S&L\end{array}\right)$
title_sort h-prime and h-semiprime ideals in $\gamma_{n}$-semirings and matrix semiring $\left(\begin{array}{ll}r&\gamma\\s&l\end{array}\right)$
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2009-10-01
description 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.
url http://www.armjmath.sci.am/index.php/ajm/article/view/58
work_keys_str_mv AT kumarsardarsujit hprimeandhsemiprimeidealsingammansemiringsandmatrixsemiringleftbeginarrayllrgammaslendarrayright
AT chandrasahabibhas hprimeandhsemiprimeidealsingammansemiringsandmatrixsemiringleftbeginarrayllrgammaslendarrayright
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