JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 88-92.doi: 10.6040/j.issn.1671-9352.0.2021.683

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Finitely Gorenstein copresented comodules over triangular matrix coalgebras

GUO Chun-na, YAO Hai-lou*   

  1. Department of Science, College of Mathematics, Bejing University of Technology, Bejing 100124, China
  • Published:2023-02-12

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Abstract: The specific form of the finitely Gorenstein copresented comodule over a triangular matrix coalgebra Γ=(T TMU0 U)is given by the equivalence theorem of categories and the exact functors between categories, and a relationship between the finitely Gorenstein copresented dimensions of the triangular matrix coalgebra Γ and coalgebras T and U is obtained as follows Max{G.cp.dimT,G.cp.dimU}≤G.cp.dimΓ≤G.cp.diimT+G.cp.dimU+1.

Key words: triangular matrix coalgebra, finitely Gorenstein copresented comodule, finitely Gorenstein co-presented dimension

CLC Number: 

  • O153.3
[1] WANG M, WU Z. Conoetherian coalgebras[J]. Algebra Colloquium, 1998, 5(1):117-120.
[2] ASENSIO M J, LÓPEZ RAMOS J A, TORRECILLAS B. Gorenstein coalgebras[J]. Acta Mathematica Hungarica, 1999, 85(1):187-198.
[3] AUSLANDER M, REITEN I, SMALO S. Representation theory of Artin algebra[J]. Cambridge Studies in Adv Math, 1995: 1-190.
[4] KOSAKOWSKA J, SIMSON D. Bipartite coalgebras and a reduction functor for coradical square complete coalgebras[J]. Colloq Math, 2008, 112(1):89-129.
[5] IOVANOV M. Triangular matrix coalgebras and applications[J]. Linear and Multilinear Algebra, 2015, 63(1):46-67.
[6] DOI Y. Homological coalgebra[J]. J Math Soc Japan, 1981, 33:31-50.
[1] FU Xue-rong, YAO Hai-lou. Tilting comodules over triangular matrix coalgebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 25-29.
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