IJPAM: Volume 97, No. 1 (2014)

GRADED SUBMODULES WITH PSEUDO IRREDUCIBLE,
PSEUDO PRIME AND STRICTLY NON-PRIME COMPONENTS

Rashid Abu-Dawwas$^1$, Khaldoun Al-Zoubi$^2$
$^1$Department of Mathematics
Yarmouk University
Irbid, JORDAN
$^2$Department of Mathematics and Statistics
Jordan University of Science and Technology
Irbid, JORDAN


Abstract. Let $G$ be a group. Let $R$ be a commutative $G$-graded ring, $M$ be a graded $R$-module and $N$ be a graded $R$-submodule of $M$. In this paper, we study some cases when $R$ is strongly graded ring and the component $N_{e}$ of $N$ is strictly non-prime, pseudo prime or pseudo irreducible $R_{e}$-submodule. For example, we prove that if $R$ is strongly graded, the components of $M$ are multiplication and $N_{e}$ is pseudo irreducible, then $N_{g}$ is pseudo prime for all $g\in G$.

Received: June 5, 2014

AMS Subject Classification: 13A02, 16W50

Key Words and Phrases: graded modules, pseudo prime graded submodules, multiplication modules

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DOI: 10.12732/ijpam.v97i1.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 1
Pages: 31 - 35


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