JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 25-29.doi: 10.6040/j.issn.1671-9352.0.2015.297

Previous Articles     Next Articles

Tilting comodules over triangular matrix coalgebras

FU Xue-rong, YAO Hai-lou*   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Received:2015-06-23 Online:2016-04-20 Published:2016-04-08

PDF (PC)

1114

Abstract: Based on the canonical methods of homological algebra, by studying tilting injective comodule over triangular matrix coalgebras, the lower and upper bounds of the right tilting global dimensions of these coalgebras is obtained.

Key words: right tilting global dimension, tilting comodule, Triangular matrix coalgebra

CLC Number: 

  • O153.3
[1] CHEN Jianlong, ZHANG Xiaoxiang. On modules over formal triangular matrix rings[J]. East-West J Math, 2001, 3:69-77.
[2] HAGHANY A, VARADARAJAN K. Study of formal triangular matrix rings[J]. Comm Algebra, 1999, 27:5507-5525.
[3] HAGHANY A, VARADARAJAN K. Study of modules over formal triangular matrix rings[J]. J Pure Appl Algebra, 2000, 147:41-58.
[4] AUSLANDER M, REITEN I, SMALO S O. Representation theory of Artin algebras[M]. Cambridge: Cambridge University Press, 1995.
[5] DOI Y. Homological coalgebra[J]. J Math Soc Japan, 1981, 33:31-50.
[6] ENOCHS E E, LÓPEZ RAMOS J A. Relative homological coalgebras[J]. Acta Math Hungar, 2004, 104(4):331-343.
[7] TAKEUCHI M. Morita theorems for categories of comodules[J]. J Fac Sci Univ Tokyo, 1977, 24(3):629-644.
[8] KOSAKOWSKA J, SIMSON D. Bipartite coalgebras and a reduction functor for coradical square complete coalgebras[J]. Colloq Math, 2008, 112(1):89-129.
[9] IOVANOV M C. Triangular matrix coalgebras and applications[J]. Linear and Multilinear Algebra, 2015, 63(1):46-67.
[10] TORRECILLAS J G. Some co-hom functors and classical tilting comodules[J]. SEA Bull Math, 1998, 22:455-468.
[11] WANG Mingyi. Tilting comodules over semi-perfect coalgebras[J]. Algebra Colloq, 1999, 6:461-472.
[12] TANG Gaohua, LI Chunna, ZHOU Yiqiang. Study of Morits contexts[J]. Comm Algebra, 2014, 42:1668-1681.
[13] CUADRA J, TORRECILLAS J G. Serial coalgebras[J]. J Pure Appl Algebra, 2004, 189:89-107.
[14] FOSSUM R, GRIFFITH P, REITEN I. Trivial extensions of abelian categories[M]. New York: Springer-Verlag, 1975.
[1] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[2] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15.
[3] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[4] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[5] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[6] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[7] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[8] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35.
[9] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23.
[10] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
[11] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.
[12] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[13] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.
[14] GAO Han-peng, YIN Xiao-bin. On strongly g(x)-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 24-29.
[15] WANG Yao, ZHOU Yun, REN Yan-li. Strongly 2-good Rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 14-18.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd