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- 2016
三角矩阵余代数上的倾斜余模
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Abstract:
摘要: 基于经典的同调代数方法,通过研究三角矩阵余代数上的倾斜内射余模, 得到三角矩阵余代数的右倾斜整体维数的上、下界。
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
[1] | AUSLANDER M, REITEN I, SMALO S O. Representation theory of Artin algebras[M]. Cambridge: Cambridge University Press, 1995. |
[2] | TAKEUCHI M. Morita theorems for categories of comodules[J]. J Fac Sci Univ Tokyo, 1977, 24(3):629-644. |
[3] | WANG Mingyi. Tilting comodules over semi-perfect coalgebras[J]. Algebra Colloq, 1999, 6:461-472. |
[4] | CHEN Jianlong, ZHANG Xiaoxiang. On modules over formal triangular matrix rings[J]. East-West J Math, 2001, 3:69-77. |
[5] | HAGHANY A, VARADARAJAN K. Study of formal triangular matrix rings[J]. Comm Algebra, 1999, 27:5507-5525. |
[6] | HAGHANY A, VARADARAJAN K. Study of modules over formal triangular matrix rings[J]. J Pure Appl Algebra, 2000, 147:41-58. |
[7] | IOVANOV M C. Triangular matrix coalgebras and applications[J]. Linear and Multilinear Algebra, 2015, 63(1):46-67. |
[8] | DOI Y. Homological coalgebra[J]. J Math Soc Japan, 1981, 33:31-50. |
[9] | KOSAKOWSKA J, SIMSON D. Bipartite coalgebras and a reduction functor for coradical square complete coalgebras[J]. Colloq Math, 2008, 112(1):89-129. |
[10] | TORRECILLAS J G. Some co-hom functors and classical tilting comodules[J]. SEA Bull Math, 1998, 22:455-468. |
[11] | ENOCHS E E, LóPEZ RAMOS J A. Relative homological coalgebras[J]. Acta Math Hungar, 2004, 104(4):331-343. |
[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. |