Bounds on Bass numbers and their dual
Abolfazl Tehranian; Siamak Yassemi
Archivum Mathematicum (2007)
- Volume: 043, Issue: 4, page 259-263
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topTehranian, Abolfazl, and Yassemi, Siamak. "Bounds on Bass numbers and their dual." Archivum Mathematicum 043.4 (2007): 259-263. <http://eudml.org/doc/250152>.
@article{Tehranian2007,
abstract = {Let $(R,\mathfrak \{m\})$ be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated $R$-module.},
author = {Tehranian, Abolfazl, Yassemi, Siamak},
journal = {Archivum Mathematicum},
keywords = {Bass numbers; injective dimension; zero dimensional rings; Bass numbers; injective dimension; zero dimensional rings},
language = {eng},
number = {4},
pages = {259-263},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Bounds on Bass numbers and their dual},
url = {http://eudml.org/doc/250152},
volume = {043},
year = {2007},
}
TY - JOUR
AU - Tehranian, Abolfazl
AU - Yassemi, Siamak
TI - Bounds on Bass numbers and their dual
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 4
SP - 259
EP - 263
AB - Let $(R,\mathfrak {m})$ be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated $R$-module.
LA - eng
KW - Bass numbers; injective dimension; zero dimensional rings; Bass numbers; injective dimension; zero dimensional rings
UR - http://eudml.org/doc/250152
ER -
References
top- Avramov L. L., Sur la croissance des nombres de Betti d’un anneau local, C. R. Acad. Sci. Paris 289 (1979), 369–372. (1979) Zbl0425.13009MR0554947
- Bass H., On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8–28. (1963) Zbl0112.26604MR0153708
- Bican L., El Bashir R., Enochs E. E., All modules have flat covers, Bull. London Math. Soc. 33 (2001), 385–390. Zbl1029.16002MR1832549
- Enochs E. E., Flat covers and flat cotorsion modules, Proc. Amer. Math. Soc. 92 (1984), 179–184. (1984) Zbl0522.13008MR0754698
- Enochs E. E., Jenda O. M. G., Relative homological algebra, de Gruyter Expositions in Mathematics, 30. Walter de Gruyter & Co., Berlin, 2000. MR1753146
- Enochs E. E., Xu J. Z., On invariants dual to the Bass numbers, Proc. Amer. Math. Soc. 125 (1997), 951–960. (1997) Zbl0868.13011MR1363457
- 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. (1975) Zbl0321.13013MR0396529
- Foxby H.-B., On the in a minimal injective resolution, Math. Scand. 29 (1971), 175–186. (1971) MR0309919
- Gulliksen T., A proof of the existence of minimal R-algebra resolutions, Acta Math. 120 (1968), 53–58. (1968) Zbl0157.34603MR0224607
- Ramras M., Bounds on Betti numbers, Canad. J. Math. 34 (1982), 589–592. (1982) Zbl0512.13008MR0663305
- Roberts P., Two applications of dualizing complexes over local rings, Ann. Sci. École Norm. Sup. (4) 9 (1), (1976), 103–106. (1976) Zbl0326.13004MR0399075
- Roberts P., Rings of type 1 are Gorenstein, Bull. London Math. Soc. 15 (1983), 48–50. (1983) Zbl0487.13008MR0686348
- Xu J. Z., Minimal injective and flat resolutions of modules over Gorenstein rings, J. Algebra 175 (1995), 451–477. (1995) Zbl0827.13005MR1339651
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.