Geodesic
$Gr$-injective modules and $gr$-projective modules over $G$-graded commutative rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 172-193 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is well known that the decomposition of injective modules over noetherian rings and the decomposition of projective modules over artinian rings are among the most beautiful and important results in commutative algebra. Our aim is to prove similar results for graded rings. It is important for us to understand the structure of the modules over the graded rings. In this paper, we study the structure theorem for $gr$-injective modules over $gr$-noetherian $G$-graded commutative rings and the structure theorem for $gr$-projective modules over $gr$-artinian $G$-graded commutative rings. 
@article{ZNSL_2019_478_a7,
     author = {Li Lu},
     title = {$Gr$-injective modules and $gr$-projective modules over $G$-graded commutative rings},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a7/}
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Li Lu. $Gr$-injective modules and $gr$-projective modules over $G$-graded commutative rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 172-193. http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a7/

[1] D. D. Anderson, D. F. Anderson, “Divisibility properties of graded domains”, Canad. J. Math., 34:1 (1982), 196–215 | DOI | MR | Zbl

[2] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, Springer Science Business Media, 2012 | MR

[3] M. F. Atiyah, I. G. MacDonald, Introduction to commutative algebra, Westview Press, 2018 | MR

[4] D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer-Verlag, 1995 | MR | Zbl

[5] S. Goto, K. Yamagishi, “Finite generation of Noetherian graded rings”, Proceedings of the American Mathematical Society, 89:1 (1983), 41–44 | DOI | MR | Zbl

[6] W. Heinzer, M. Roitman, “The homogeneous spectrum of a graded commutative ring”, Proc. Amer. Math. Soc., 130:6 (2001), 1573–1580 | DOI | MR

[7] C. Nastasescu, F. Van Oystaeyen, Methods of Graded Rings, Springer, 2004 | MR | Zbl

[8] C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory, Elsevier, 2011 | MR

[9] C. Park, M. Park, “Integral closure of a graded Noetherian domain”, J. the Korean Math. Soc., 48:3 (2011), 449–464 | DOI | MR | Zbl

[10] L. J. Ratliff, D. E. Rush, “Two notes on homogeneous prime ideals in graded Noetherian rings”, J. Algebra, 264:1 (2003), 211–230 | DOI | MR | Zbl

[11] J. Rotman, An Introduction to Homological Algebra, Springer, 1988 | MR

[12] D. E. Rush, “Noetherian properties in monoid rings”, J. Pure and Applied Algebra, 185:1–3 (2003), 259–278 | DOI | MR | Zbl

[13] I. N. Balaba, “Koltsa chastnykh graduirovannykh assotsiativnykh kolets. I”, Fundamentalnaya i prikladnaya matematika, 17:2 (2012), 3–74 | MR | Zbl