Abstract:
For finite modules over a local ring the general problem is considered of finding an extension of the class of modules of finite projective dimension preserving various properties. In the first section the concept of a suitable complex is introduced, which is a generalization of both a dualizing complex and a suitable module. Several properties of the dimension of modules
with respect to such complexes are established. In particular, a generalization of Golod's theorem on the behaviour of GK-dimension with respect to a suitable module K under factorization by ideals of a special kind is obtained and a new form of the Avramov–Foxby conjecture on the transitivity of G-dimension is suggested. In the second section a class of modules containing modules of finite CI-dimension is considered, which has some additional properties. A dimension constructed in the third section characterizes the Cohen–Macaulay rings in precisely the same way as the class of modules of finite projective dimension characterizes regular rings and the class of modules of finite CI-dimension characterizes complete intersections.
This publication is cited in the following 48 articles:
Dipankar Ghosh, Aniruddha Saha, “Homological dimensions of Burch ideals, submodules and quotients”, Journal of Pure and Applied Algebra, 228:7 (2024), 107647
Michal Hrbek, Giovanna Le Gros, “Restricted Injective Dimensions over Cohen-Macaulay Rings”, Algebr Represent Theor, 2024
Cleto B. Miranda-Neto, Thyago S. Souza, “On reduced G-perfection and horizontal linkage”, Communications in Algebra, 52:3 (2024), 978
Takeshi Yoshizawa, “Annihilators of local cohomology modules via a classification theorem of the dominant resolving subcategories”, Communications in Algebra, 51:3 (2023), 939
Olgur Celikbas, Li Liang, Arash Sadeghi, Tirdad Sharif, “A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula”, Acta. Math. Sin.-English Ser., 39:3 (2023), 439
Glenn Ando, “Annihilators of local cohomology modules and restricted flat dimensions”, Communications in Algebra, 51:3 (2023), 991
Dehghani-Zadeh F., Dibaei M.T., Sadeghi A., “Linkage of Modules By Reflexive Morphisms”, J. Math. Soc. Jpn., 74:1 (2022), 25–77
Ryo Takahashi, “Classification of dominant resolving subcategories by moderate functions”, Illinois J. Math., 65:3 (2021)
Araya T., “A Homological Dimension Related to Ab Rings”, Beitr. Algebr. Geom., 60:2 (2019), 225–231
Mohammad T. Dibaei, Arash Sadeghi, “Linkage of modules with respect to a semidualizing module”, Pacific J. Math., 294:2 (2018), 307
Sadeghi A., J. Pure Appl. Algebr., 221:6 (2017), 1344–1365
Sanders W., “Classifying resolving subcategories”, Pac. J. Math., 286:2 (2017), 401–438
Liang L., Yang G., “Lower complete intersection dimension over local homomorphisms”, Indian J. Pure Appl. Math., 47:4 (2016), 673–686
Nasseh S., Sather-Wagstaff S., “Cohen Factorizations: Weak Functoriality and Applications”, J. Pure Appl. Algebr., 219:3, SI (2015), 622–645
Tokuji Araya, Kei-Ichiro Iima, Ryo Takahashi, “On the Left Perpendicular Category of the Modules of Finite Projective Dimension”, Communications in Algebra, 40:8 (2012), 2693
Yoshizawa T., “On Gorenstein Injectivity of TOP Local Cohomology Modules”, Proc. Amer. Math. Soc., 140:6 (2012), 1897–1907
Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm, Commutative Algebra, 2011, 101
Sazeedeh R., “Gorenstein injectivity of the section functor”, Forum Mathematicum, 22:6 (2010), 1117–1127
Citation in format AMSBIB
Contact us: