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Gr-Injective Modules and gr-Projective Modules Over G-Graded Commutative Rings

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It is well known that the decomposition of injective modules over Noether rings and the decomposition of projective modules over Artinian rings are some of the most beautiful and important results in commutative algebra. The goal of the paper is to prove similar results for graded rings; this is important to understand the structure of modules over graded rings. The obtained results include structural theorems for gr-injective modules over gr-Noetherian G-graded commutative rings and for gr-finitely generated gr-projective modules over gr-Artinian G-graded commutative rings. Bibliography: 13 titles.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    L. Lu

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  1. L. Lu
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Correspondence to L. Lu.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 478, 2019, pp. 172–193.

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Lu, L. Gr-Injective Modules and gr-Projective Modules Over G-Graded Commutative Rings. J Math Sci 247, 613–625 (2020). https://doi.org/10.1007/s10958-020-04823-z

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  • DOI: https://doi.org/10.1007/s10958-020-04823-z

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