Geodesic
EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 85-96

Voir la notice de l'article provenant de la source Cambridge University Press

This paper builds on work of Hochster and Yao that provides nice embeddings for finitely generated modules of finite G-dimension, finite projective dimension or locally finite injective dimension. We extend these results by providing similar embeddings in the relative setting, that is, for certain modules of finite GC-dimension, finite C-projective dimension, locally finite C-injective dimension or locally finite C-injective dimension where C is a semidualizing module. Along the way, we extend some results for modules of finite homological dimension to modules of locally finite homological dimension in the relative setting.
DOI : 10.1017/S0017089512000353
Mots-clés : 13D02, 13D05, 13D07 
SATHER-WAGSTAFF, SEAN. EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 85-96. doi: 10.1017/S0017089512000353
@article{10_1017_S0017089512000353,
     author = {SATHER-WAGSTAFF, SEAN},
     title = {EMBEDDING {MODULES} {OF} {FINITE} {HOMOLOGICAL} {DIMENSION}},
     journal = {Glasgow mathematical journal},
     pages = {85--96},
     year = {2013},
     volume = {55},
     number = {1},
     doi = {10.1017/S0017089512000353},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000353/}
}
TY  - JOUR
AU  - SATHER-WAGSTAFF, SEAN
TI  - EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION
JO  - Glasgow mathematical journal
PY  - 2013
SP  - 85
EP  - 96
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000353/
DO  - 10.1017/S0017089512000353
ID  - 10_1017_S0017089512000353
ER  - 
%0 Journal Article
%A SATHER-WAGSTAFF, SEAN
%T EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION
%J Glasgow mathematical journal
%D 2013
%P 85-96
%V 55
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000353/
%R 10.1017/S0017089512000353
%F 10_1017_S0017089512000353

[1] 1.Auslander, M., Anneaux de Gorenstein, et torsion en algèbre commutative, in Séminaire d'algèbre commutative dirigé par pierre samuel, vol. 1966/67 (Secrétariat mathématique, Paris, 1967), MR 37 #1435. Google Scholar

[2] 2.Auslander, M. and Bridger, M., Stable module theory, Memoirs of the American Mathematical Society, No. 94 (Amer. Math. Soc., Providence, RI, 1969), MR 42 #4580. Google Scholar | DOI

[3] 3.Avramov, L. L. and Buchweitz, R.-O., Support varieties and cohomology over complete intersections, Invent. Math. 142 (2) (2000), 285–318. MR 1794064 (2001j:13017). Google Scholar

[4] 4.Avramov, L. L., Iyengar, S. B. and Lipman, J., Reflexivity and rigidity for complexes. I. Commutative rings, Algebra Number Theory 4 (1) (2010), 47–86. MR 2592013. Google Scholar | DOI

[5] 5.Avramov, L. L. and Martsinkovsky, A., Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. London Math. Soc. 85 (3) (2002), 393–440. MR 2003g:16009. Google Scholar

[6] 6.Christensen, L. W., Frankild, A. and Holm, H., On Gorenstein projective, injective and flat dimensions—A functorial description with applications, J. Algebra 302 (1) (2006), 231–279. MR 2236602. Google Scholar

[7] 7.Enochs, E. E. and Jenda, O. M. G., Gorenstein injective and projective modules, Math. Z. 220 (4) (1995), 611–633. MR 1363858 (97c:16011). Google Scholar

[8] 8.Enochs, E. E., Jenda, O. M. G. and Xu, J. Z., Foxby duality and Gorenstein injective and projective modules, Trans. Amer. Math. Soc. 348 (8) (1996), 3223–3234. MR 1355071 (96k:13010). Google Scholar

[9] 9.Foxby, H.-B., Gorenstein modules and related modules, Math. Scand. 31 (1972), 267–284. MR 48 #6094. Google Scholar | DOI

[10] 10.Foxby, H.-B., Gorenstein dimensions over Cohen-Macaulay rings, in Proceedings of the international conference on commutative algebra (Bruns, W., Editor) (Universität Osnabrück, Osnabrück, Germany, 1994), 59–63. Google Scholar

[11] 11.Frankild, A. and Sather-Wagstaff, S., Reflexivity and ring homomorphisms of finite flat dimension, Commun. Algebra 35 (2) (2007), 461–500. MR 2294611. Google Scholar | DOI

[12] 12.Golod, E. S., G-dimension and generalized perfect ideals, in Algebraic geometry and its applications, vol. 165 (Trudy Mat. Inst. Steklova, 1984), 62–66, MR 85m:13011. Google Scholar

[13] 13.Hartshorne, R., Residues and duality, Lecture Notes in Mathematics, vol. 20 (Springer-Verlag, Berlin, 1966). MR 36 #5145. Google Scholar | DOI

[14] 14.Hochster, M. and Yao, Y., An embedding theorem for modules of finite (G-)projective dimension, preprint (2009). Google Scholar

[15] 15.Holm, H. and Jørgensen, P., Semidualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2) (2006), 423–445. MR 2203625. Google Scholar

[16] 16.Holm, H. and White, D., Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (4) (2007), 781–808. MR 2413065. Google Scholar

[17] 17.Sather-Wagstaff, S., Bass numbers and semidualizing complexes, in Commutative algebra and its applications (Walter de Gruyter, Berlin, 2009), 349–381. MR 2640315. Google Scholar

[18] 18.Sather-Wagstaff, S., Sharif, T. and White, D., Tate cohomology with respect to semidualizing modules, J. Algebra 324 (9) (2010), 2336–2368. MR 2684143. Google Scholar

[19] 19.Takahashi, R. and White, D., Homological aspects of semidualizing modules, Math. Scand. 106 (1) (2010), 5–22. MR 2603458. Google Scholar | DOI

[20] 20.Vasconcelos, W. V., Divisor theory in module categories (North-Holland Publishing Co., Amsterdam, 1974), North-Holland Mathematics Studies, No. 14, Notas de Matemática No. 53. [Notes on Mathematics, No. 53]. MR 0498530 (58 #16637). Google Scholar

[21] 21.White, D., Gorenstein projective dimension with respect to a semidualizing module, J. Commut. Algebra 2 (1) (2010), 111–137. MR 2607104. Google Scholar

Cité par Sources :