Graded modules and their completions
Maurice Auslander, Idun Reiten (1990)
Banach Center Publications
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Maurice Auslander, Idun Reiten (1990)
Banach Center Publications
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Huru, H.L. (2007)
Lobachevskii Journal of Mathematics
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Khaldoun Al-Zoubi, Amani Al-Qderat (2017)
Open Mathematics
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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.
C. Nastasescu, F. Van Oystaeyen (1990)
Mathematische Zeitschrift
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Everett C. Dade (1980)
Mathematische Zeitschrift
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Samir Mahmoud, S. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Patrik Lundström (2004)
Colloquium Mathematicae
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We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely...
C. Nastasescu, F. Van Oystaeyen (1991)
Mathematische Zeitschrift
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Luchezar L. Avramov, Jürgen Herzog (1994)
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Mathematica Scandinavica
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Tadeusz Józefiak (1976)
Fundamenta Mathematicae
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Peter Jørgensen (2003)
Fundamenta Mathematicae
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Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.
Morton E. Harris (1987)
Mathematische Zeitschrift
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Huq, S.A., Aijaz, Kulsoom (1969)
Portugaliae mathematica
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