On graded second and coprimary modules and graded secondary representations. (English) Zbl 1338.16046
Summary: In this paper, we introduce and study the concepts of graded second (gr-second) and graded coprimary (gr-coprimary) modules which are different from second and coprimary modules over arbitrary-graded rings. We list some properties and characterizations of gr-second and gr-coprimary modules and also study graded prime submodules of modules with gr-coprimary decompositions. We also deal with graded secondary representations for graded injective modules over commutative-graded rings. By using the concept of \(\sigma\)-suspension \((\sigma)M\) of a graded module \(M\), we prove that a graded injective module over a commutative graded Noetherian ring has a graded secondary representation.
MSC:
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16D10 | General module theory in associative algebras |
| 13A02 | Graded rings |
| 13C11 | Injective and flat modules and ideals in commutative rings |
Keywords:
graded second modules; graded coprimary modules; graded prime submodules; graded primary ideals; graded secondary modules; graded injective modulesReferences:
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