Syzygies and Homological Conjectures

1989 ◽  
pp. 139-156 ◽  
Author(s):  
S. P. Dutta
Keyword(s):  
Homological Conjectures

scholarly journals AUSLANDER GENERATORS AND HOMOLOGICAL CONJECTURES

2013 ◽  
Vol 56 (3) ◽  
pp. 503-506 ◽  
Author(s):  
JIAQUN WEI
Keyword(s):  
Artin Algebra ◽  
Representation Dimension ◽  
Homological Conjectures

AbstractLet A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

scholarly journals Homological conjectures, old and new

2007 ◽  
Vol 51 (1) ◽  
pp. 151-169 ◽  
Author(s):  
Melvin Hochster
Keyword(s):  
Homological Conjectures

scholarly journals Toward the construction of big Cohen-Macaulay modules

1986 ◽  
Vol 103 ◽  
pp. 95-125 ◽  
Author(s):  
Yuji Yoshino
Keyword(s):  
General Setting ◽  
Local Rings ◽  
Remarkable Progress ◽  
Homological Conjectures

What we call the homological conjectures on commutative Noetherian local rings were first collected and partially settled by C. Peskine and L. Szpiro [PS1]. The subsequent remarkable progress was made by M. Hochster [H1] who conjectured the existence of big Cohen-Macaulay modules and solved it in the affirmative for equicharacteristic local rings. It is, however, still open in general setting.

Sign in / Sign up

Export Citation Format

Share Document