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| 1 | Frobenius bimodules and flat-dominant dimensions显示文摘We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita. | Changchang Xi | 2021 | Science China Mathematics2021，64，1： | 6 |
| 2 | ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS显示文摘ONΔ┐GOODMODULECATEGORIESOFQUASI┐HEREDITARYALGEBRAS**DENGBANGMING*XICHANGCHANG*ManuscriptreceivedJune12,1995.RevisedMay3,1996.... | DENG BANGMING * XI CHANGCHANG * | 1997 | Chinese Annals of Mathematics,Series B1997，18，4： | 2 |
| 3 | A characterization of the tilting pair显示文摘 | WEI Jiaqun XI Changchang | 2007 | J Algebra2007，317，： | 1 |
| 4 | Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube显示文摘 | Steffen K?nig Changchang Xi | 1998 | Communications in Mathematical Physics1998，，2： | 1 |
| 5 | Auslander-Reiten correspondence for tilting pairs显示文摘 | WEI Jiaqun XI Changchang | 2008 | J Pure Applied Algebra2008，212，： | 1 |
| 6 | Quasi-hereditary algebras which are twisted double incidence algebras of posets 显示文摘 | DENG Bangming XI Changchang | 1995 | Contri Alg Geom1995，36，： | 1 |
| 7 | Quasi-hereditary algebras which are dual extensions of algebras显示文摘 | DENG Bangming XI Changchang | 1994 | Comm Alg1994，22，： | 1 |
| 8 | Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube显示文摘 | Steffen K?nig Changchang Xi | 1998 | Communications in Mathematical Physics1998，，2： | 1 |
| 9 | The number of simple modules of a cellular algebra显示文摘Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix. | LI Weixia XI Changchang | 2005 | Science China Mathematics2005，48，6： | 1 |
| 10 | Quadratic forms for △-good module categories of quasi-hereditary algebras显示文摘 | Liu Shaoxue Xi Changchang | 1999 | Comm Algebra1999，27，： | 1 |
| 11 | p-Radical in BCI-algebras显示文摘 | LEI Tiande XI Changchang | 1985 | Math Japonica1985，30，4： | 1 |
| 12 | On a class of BCI-algebras显示文摘 | XI Changchang | 1990 | Math Japonica1990，35，1： | 1 |
| 13 | On the finitistic dimension conjecture II: Related to finite global dimension显示文摘 | Changchang Xi | 2005 | Advances in Mathematics2005，，1： | 1 |
| 14 | Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube显示文摘 | Steffen K?nig Changchang Xi | 1998 | Communications in Mathematical Physics1998，，2： | 1 |
| 15 | Strong Symmetry Defined by Twisting Modules, Applied to Quasi-Hereditary Algebras with Triangular Decomposition and Vanishing Radical Cube显示文摘 | Steffen K?nig Changchang Xi | 1998 | Communications in Mathematical Physics1998，，2： | 1 |
| 16 | Global dimensions of dual extension algebras显示文摘 | Changchang Xi | 1995 | Manuscripta Mathematica1995，，1： | 1 |
| 17 | A characterization of the tilting pair显示文摘 | Jiaqun Wei Changchang Xi | 2007 | Journal of Algebra2007，，1： | 1 |
| 18 | D-split sequences and derived equivalences显示文摘 | Wei HU Changchang XI | | 0，，01： | 1 |
| 19 | A characterization of the tilting pair显示文摘 | WEI Jiaqun XI Changchang | 2007 | J Algebra2007，317，： | 1 |
| 20 | Auslander-Reiten correspondence for tilting pairs显示文摘 | WEI Jiaqun XI Changchang | 2008 | J Pure Applied Algebra2008，212，： | 1 |
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