Keywords: Bass numbers; injective dimension; zero dimensional rings
@article{ARM_2007_43_4_a3,
author = {Tehranian, Abolfazl and Yassemi, Siamak},
title = {Bounds on {Bass} numbers and their dual},
journal = {Archivum mathematicum},
pages = {259--263},
year = {2007},
volume = {43},
number = {4},
mrnumber = {2378526},
zbl = {1155.13303},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_4_a3/}
}
Tehranian, Abolfazl; Yassemi, Siamak. Bounds on Bass numbers and their dual. Archivum mathematicum, Tome 43 (2007) no. 4, pp. 259-263. http://geodesic.mathdoc.fr/item/ARM_2007_43_4_a3/
[1] Avramov L. L.: Sur la croissance des nombres de Betti d’un anneau local. C. R. Acad. Sci. Paris 289 (1979), 369–372. | MR | Zbl
[2] Bass H.: On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–28. | MR | Zbl
[3] Bican L., El Bashir R., Enochs E. E.: All modules have flat covers. Bull. London Math. Soc. 33 (2001), 385–390. | MR | Zbl
[4] Enochs E. E.: Flat covers and flat cotorsion modules. Proc. Amer. Math. Soc. 92 (1984), 179–184. | MR | Zbl
[5] Enochs E. E., Jenda O. M. G.: Relative homological algebra. de Gruyter Expositions in Mathematics, 30. Walter de Gruyter & Co., Berlin, 2000. | MR
[6] Enochs E. E., Xu J. Z.: On invariants dual to the Bass numbers. Proc. Amer. Math. Soc. 125 (1997), 951–960. | MR | Zbl
[7] Fossum R., Foxby H.-B., Griffith P., Reiten I.: Minimal injective resolutions with applications to dualizing modules and Gorenstein modules. Inst. Hautes Études Sci. Publ. Math. 45 (1975), 193–215. | MR | Zbl
[8] Foxby H.-B.: On the $\mu ^{i}$ in a minimal injective resolution. Math. Scand. 29 (1971), 175–186. | MR
[9] Gulliksen T.: A proof of the existence of minimal R-algebra resolutions. Acta Math. 120 (1968), 53–58. | MR | Zbl
[10] Ramras M.: Bounds on Betti numbers. Canad. J. Math. 34 (1982), 589–592. | MR | Zbl
[11] Roberts P.: Two applications of dualizing complexes over local rings. Ann. Sci. École Norm. Sup. (4) 9 (1), (1976), 103–106. | MR | Zbl
[12] Roberts P.: Rings of type 1 are Gorenstein. Bull. London Math. Soc. 15 (1983), 48–50. | MR | Zbl
[13] Xu J. Z.: Minimal injective and flat resolutions of modules over Gorenstein rings. J. Algebra 175 (1995), 451–477. | MR | Zbl