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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 478, Pages 172–193
(Mi znsl6749)
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$Gr$-injective modules and $gr$-projective modules over $G$-graded commutative rings
Li Lu Lomonosov Moscow State University,
Department of Mechanics and Mathematics,
GSP-1, Leninskie Gory, 119991
Moscow, Russian Federation
Abstract:
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.
Key words and phrases:
graded commutative rings, $gr$-injective modules, $gr$-projective modules.
Received: 29.04.2019
Citation:
Li Lu, “$Gr$-injective modules and $gr$-projective modules over $G$-graded commutative rings”, Problems in the theory of representations of algebras and groups. Part 34, Zap. Nauchn. Sem. POMI, 478, POMI, St. Petersburg, 2019, 172–193
Linking options:
https://www.mathnet.ru/eng/znsl6749 https://www.mathnet.ru/eng/znsl/v478/p172
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Statistics & downloads: |
Abstract page: | 175 | Full-text PDF : | 32 | References: | 15 |
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