[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j200443

THE GORENSTEIN TRANSPOSE OF COMODULES

Li, Yexuan (College of Mathematics, Faculty of Science Beijing University of Technology)
Yao, Hailou (College of Mathematics, Faculty of Science Beijing University of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 1019-1033 More about this Journal

Abstract

Let 𝚪 be a Gorenstein coalgebra over a filed k. We introduce the Gorenstein transpose via a minimal Gorenstein injective copresentation of a quasi-finite 𝚪-comodule, and obtain a relation between a Gorenstein transpose of a quasi-finite comodule and a transpose of the same comodule. As an application, we obtain that the almost split sequences are constructed in terms of Gorenstein transpose.

Keywords

Gorenstein coalgebra; Gorenstein injective comodule; transpose; almost split sequence;

Citations & Related Records

Reference

1	M. J. Asensio, J. A. L'opez Ramos, and B. Torrecillas, Gorenstein coalgebras, Acta Math. Hungar. 85 (1999), no. 1-2, 187-198. https://doi.org/10.1023/A:1006697618613 DOI
2	W. Chin, M. Kleiner, and D. Quinn, Almost split sequences for comodules, J. Algebra 249 (2002), no. 1, 1-19. https://doi.org/10.1006/jabr.2001.9086 DOI
3	M. Takeuchi, Morita theorems for categories of comodules, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 3, 629-644.
4	C. Huang and Z. Huang, Gorenstein syzygy modules, J. Algebra 324 (2010), no. 12, 3408-3419. https://doi.org/10.1016/j.jalgebra.2010.10.010 DOI
5	M. Auslander and M. Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, RI, 1969.
6	M. Auslander, I. Reiten, and S. O. Smalo, Representation theory of Artin algebras, corrected reprint of the 1995 original, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, Cambridge, 1997.
7	W. Chin and D. Simson, Coxeter transformation and inverses of Cartan matrices for coalgebras, J. Algebra 324 (2010), no. 9, 2223-2248. https://doi.org/10.1016/j.jalgebra.2010.06.029 DOI
8	E. E. Enochs and J. A. L'opez-Ramos, Relative homological coalgebras, Acta Math. Hungar. 104 (2004), no. 4, 331-343. https://doi.org/10.1023/B:AMHU.0000036293. 46154.4e DOI
9	Q. X. Pan and Q. Li, On Gorenstein injective and projective comodules, Math. Notes 94 (2013), no. 1-2, 255-265. https://doi.org/10.1134/S0001434613070250 DOI
10	F. Meng, (Weakly) Gorenstein injective and (weakly) Gorenstein coflat comodules, Studia Sci. Math. Hungar. 49 (2012), no. 1, 106-119. https://doi.org/10.1556/SScMath.2011.1189 DOI
11	M. Y. Wang, Morita Equivalence and Its Generalizations, Graduate Series in Mathematics 2, Science Press, Beijing New York, 2001.