Projective resolutions of graded modules

2001 ◽  
pp. 273-282
Author(s):  
Yves Félix ◽  
Stephen Halperin ◽  
Jean-Claude Thomas
Keyword(s):  
Graded Modules ◽  
Projective Resolutions

scholarly journals Generating degrees for graded projective resolutions

2018 ◽  
Vol 17 (10) ◽  
pp. 1850191 ◽  
Author(s):  
Eduardo N. Marcos ◽  
Andrea Solotar ◽  
Yury Volkov
Keyword(s):  
Tensor Products ◽  
Projective Resolution ◽  
Graded Algebras ◽  
Graded Modules ◽  
Projective Resolutions

We provide a framework connecting several well-known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras. Finally, we provide a tool to evaluate the possible degrees of a module appearing in a graded projective resolution once the generating degrees for the first term of some particular projective resolution are known.

scholarly journals Graded Bourbaki ideals of graded modules

2021 ◽  
Author(s):  
Jürgen Herzog ◽  
Shinya Kumashiro ◽  
Dumitru I. Stamate
Keyword(s):  
Graded Modules

scholarly journals Almost graded multiplication and almost graded comultiplication modules

2020 ◽  
Vol 53 (1) ◽  
pp. 325-331
Author(s):  
Malik Bataineh ◽  
Rashid Abu-Dawwas ◽  
Jenan Shtayat
Keyword(s):  
Commutative Ring ◽  
Graded Modules

AbstractLet G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=M. We investigate several properties of these classes of graded modules.

scholarly journals Projective Resolutions of Generic Order Ideals

1997 ◽  
Vol 191 (1) ◽  
pp. 279-330
Author(s):  
Saeja Oh Kim
Keyword(s):  
Projective Resolutions ◽  
Order Ideals

On the Multiplicity and the Cohen–Macaulayness of Fiber Cones of Graded Modules

2021 ◽  
Vol 28 (01) ◽  
pp. 13-32
Author(s):  
Nguyen Tien Manh
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Primary Ideal ◽  
Graded Algebra ◽  
Finitely Generated ◽  
Ideal Formula ◽  
Noetherian Local Ring ◽  
Graded Modules ◽  
Fiber Cone

Let [Formula: see text] be a Noetherian local ring with maximal ideal [Formula: see text], [Formula: see text] an ideal of [Formula: see text], [Formula: see text] an [Formula: see text]-primary ideal of [Formula: see text], [Formula: see text] a finitely generated [Formula: see text]-module, [Formula: see text] a finitely generated standard graded algebra over [Formula: see text] and [Formula: see text] a finitely generated graded [Formula: see text]-module. We characterize the multiplicity and the Cohen–Macaulayness of the fiber cone [Formula: see text]. As an application, we obtain some results on the multiplicity and the Cohen–Macaulayness of the fiber cone[Formula: see text].

scholarly journals A Family of Graded Modules Associated to a Module

2008 ◽  
Vol 36 (11) ◽  
pp. 4201-4217 ◽  
Author(s):  
Futoshi Hayasaka ◽  
Eero Hyry
Keyword(s):  
Graded Modules

The picard group of a category of graded modules

1996 ◽  
Vol 24 (14) ◽  
pp. 4397-4414 ◽  
Author(s):  
Margaret Beattie ◽  
Angel del Rio
Keyword(s):  
Picard Group ◽  
Graded Modules
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