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Weak dimensions and Gorenstein weak dimensions of group rings
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 803-816
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Let $K$ be a field, and let $G$ be a group. In the present paper, we investigate when the group ring $K[G]$ has finite weak dimension and finite Gorenstein weak dimension. We give some analogous versions of Serre's theorem for the weak dimension and the Gorenstein weak dimension.
Let $K$ be a field, and let $G$ be a group. In the present paper, we investigate when the group ring $K[G]$ has finite weak dimension and finite Gorenstein weak dimension. We give some analogous versions of Serre's theorem for the weak dimension and the Gorenstein weak dimension.
DOI : 10.21136/CMJ.2021.0102-20
Classification : 16E10, 16E30, 16S34
Keywords: weak dimension; Gorenstein weak dimension; principal module; group ring 
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Xiang, Yueming. Weak dimensions and Gorenstein weak dimensions  of group rings. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 803-816. doi: 10.21136/CMJ.2021.0102-20

[1] Auslander, M.: On regular group rings. Proc. Am. Math. Soc. 8 (1957), 658-664. | DOI | MR | JFM

[2] Auslander, M., Bridger, M.: Stable Module Theory. Memoirs of the American Mathematical Society 94. American Mathematical Society, Providence (1969). | DOI | MR | JFM

[3] Bennis, D., Mahdou, N.: Global Gorenstein dimensions. Proc. Am. Math. Soc. 138 (2010), 461-465. | DOI | MR | JFM

[4] Benson, D. J., Goodearl, K. R.: Periodic flat modules, and flat modules for finite groups. Pac. J. Math. 196 (2000), 45-67. | DOI | MR | JFM

[5] Colby, R. R.: Rings which have flat injective modules. J. Algebra 35 (1975), 239-252. | DOI | MR | JFM

[6] Connell, I. G.: On the group ring. Can. J. Math. 15 (1963), 650-685. | DOI | MR | JFM

[7] Emmanouil, I.: On the finiteness of Gorenstein homological dimensions. J. Algebra 372 (2012), 376-396. | DOI | MR | JFM

[8] Enochs, E. E., Jenda, O. M. G.: Gorenstein injective and projective modules. Math. Z. 220 (1995), 611-633. | DOI | MR | JFM

[9] Glaz, S.: Commutative Coherent Rings. Lecture Notes in Mathematics 1371. Springer, Berlin (1989). | DOI | MR | JFM

[10] Govorov, V. E.: On flat modules. Sib. Mat. Zh. 6 (1965), 300-304 Russian. | MR | JFM

[11] Holm, H.: Gorenstein Homological Algebra: Ph.D. Thesis. University of Copenhagen, Copenhagen (2004). | MR

[12] Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189 (2004), 167-193. | DOI | MR | JFM

[13] Lam, T. Y.: A First Course in Noncommutative Rings. Graduate Texts in Mathematics 131. Springer, New York (2001). | DOI | MR | JFM

[14] Li, L.: Representations of modular skew group algebras. Trans. Am. Math. Soc. 367 (2015), 6293-6314. | DOI | MR | JFM

[15] Passman, D. S.: The Algebraic Structure of Group Rings. John Wiley, New York (1977). | MR | JFM

[16] Rotman, J. J.: An Introduction to Homological Algebra. Pure and Applied Mathematics 85. Academic Press, New York (1979). | DOI | MR | JFM

[17] Stammbach, U.: On the weak homological dimension of the group algebra of solvable groups. J. Lond. Math. Soc., II. Ser. 2 (1970), 567-570. | DOI | MR | JFM

[18] Swan, R. G.: Groups of cohomological dimension one. J. Algebra 12 (1969), 585-601. | DOI | MR | JFM

[19] Xiang, Y.: Homological dimensions of skew group rings. Algebra Colloq. 27 (2020), 319-330. | DOI | MR | JFM

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