Geodesic
Weakly Koszul-Like Modules
Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 93-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module $M$ is a weakly Koszul-like module if and only if it can be approximated by Koszul-like graded submodules, which is equivalent to the fact that $\mathbf G(M)$ is a Koszul-like module, where $\mathbf G(M)$ denotes the associated graded module of $M$. As applications, the relationships between the minimal graded projective resolutions of $M$ and $\mathbf G(M)$, and the Koszul-like submodules are established. Moreover, the Koszul dual of a weakly Koszul-like module is proved to be generated in degree $0$ as a graded $E(A)$-module.
Mots-clés : Koszul-like algebras, Koszul-like modules
Keywords: weakly Koszul-like modules, graded algebra, Jacobson radical, Yoneda product, projective resolution, commutative diagram, short exact sequence. 
@article{MZM_2012_91_1_a8,
     author = {Pei-Sen Chen and Jia-Feng L\"u},
     title = {Weakly {Koszul-Like} {Modules}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {93--119},
     year = {2012},
     volume = {91},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a8/}
}
TY  - JOUR
AU  - Pei-Sen Chen
AU  - Jia-Feng Lü
TI  - Weakly Koszul-Like Modules
JO  - Matematičeskie zametki
PY  - 2012
SP  - 93
EP  - 119
VL  - 91
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a8/
LA  - ru
ID  - MZM_2012_91_1_a8
ER  - 
%0 Journal Article
%A Pei-Sen Chen
%A Jia-Feng Lü
%T Weakly Koszul-Like Modules
%J Matematičeskie zametki
%D 2012
%P 93-119
%V 91
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a8/
%G ru
%F MZM_2012_91_1_a8
Pei-Sen Chen; Jia-Feng Lü. Weakly Koszul-Like Modules. Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 93-119. http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a8/

[1] M. Artin, W. F. Schelter, “Graded algebras of global dimension $3$”, Adv. in Math., 66:2 (1987), 171–216 | DOI | MR | Zbl

[2] R. Berger, “Koszulity for nonquadratic algebras”, J. Algebra, 239:2 (2001), 705–734 | DOI | MR | Zbl

[3] E. L. Green, E. N. Marcos, R. Martínez-Villa, P. Zhang, “$D$-Koszul algebras”, J. Pure Appl. Algebra, 193:1-3 (2004), 141–162 | DOI | MR | Zbl

[4] J.-W. He, D.-M. Lu, “Higher Koszul algebras and $A$-infinity algebras”, J. Algebra, 293:2 (2005), 335–362 | DOI | MR | Zbl

[5] D.-M. Lu, J. H. Palmieri, Q.-S. Wu, J. J. Zhang, “Regular algebras of dimension 4 and their $A_\infty$-Ext-algebras”, Duke Math. J., 137:3 (2007), 537–584 | MR | Zbl

[6] D.-M. Lu, J.-R. Si, “Koszulity of algebras with nonpure resolutions”, Comm. Algebra, 38:1 (2010), 68–85 | MR | Zbl

[7] Lyu Sia-Fen, “Koshulepodobnye algebry i moduli”, Matem. zametki, 2012 (to appear)

[8] S. B. Priddy, “Koszul resolutions”, Trans. Amer. Math. Soc., 152 (1970), 39–60 | DOI | MR | Zbl

[9] R. Martínez-Villa, D. Zacharia, “Approximations with modules having linear resolutions”, J. Algebra, 266:2 (2003), 671–697 | DOI | MR | Zbl

[10] E. L. Green, R. Martínez-Villa, “Koszul and Yoneda algebras”, Representation Theory of Algebras (Cocoyoc, 1994), CMS Conf. Proc., 18, Amer. Math. Soc., Providence, RI, 1996, 247–297 | MR | Zbl

[11] J.-F. Lü, “On modules with piecewise-Koszul towers”, Houston J. Math., 35:1 (2009), 185–207 | MR | Zbl

[12] J.-F. Lü, J.-W. He, D.-M. Lu, “On modules with $d$-Koszul towers”, Chinese J. Contemp. Math., 28:2 (2007), 191–200 | MR | Zbl