COHOMOLOGY AND HOMOLOGY OF ABELIAN GROUPS GRADED KOSZUL–VINBERG ALGEBRAS

2009 ◽  
Vol 06 (02) ◽  
pp. 241-266 ◽  
Author(s):  
MICHEL NGUIFFO BOYOM ◽  
F. NGAKEU
Keyword(s):  
Abelian Groups ◽  
Graded Algebras ◽  
Graded Modules ◽  
Vinberg Algebras

We study abelian groups graded (or color) Koszul–Vinberg algebras and their modules. Koszul–Vinberg cohomology and homology of these algebras are studied. As applications, we investigate some extensions of graded algebras and graded modules.

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.

DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS

2003 ◽  
Vol 68 (02) ◽  
pp. 288-306 ◽  
Author(s):  
ANDERS FRANKILD ◽  
SRIKANTH IYENGAR ◽  
PETER JØRGENSEN
Keyword(s):  
Graded Algebras ◽  
Graded Modules ◽  
Differential Graded Algebras

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

scholarly journals Graded Bourbaki ideals of graded modules

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