IJPAM: Volume 76, No. 2 (2012)
OVER MULTIPLICATION MODULES
Department of Mathematics and Statistics
Jordan University of Science and Technology
Irbid, 22110, JORDAN
Abstract. Let be an abelian group with identity , be a graded commutative ring and a graded module where all modules are unital. Various generalizations of graded prime ideals have been studied. For example, a proper graded ideal is a graded weakly (resp., almost) prime ideal if (resp., ) implies or . Throughout this work, we define that a proper graded submodule of is a graded almost prime if implies or . We show that graded almost prime submodules enjoy analogs of many of the properties of prime submodules.
Received: November 12, 2011
AMS Subject Classification: 13A02, 16W50
Key Words and Phrases: graded rings, graded multiplication modules, graded almost prime submodules
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395