scholarly journals Coreflexive Modules and Semidualizing Modules with Finite Projective Dimension

2017 ◽  
Vol 21 (6) ◽  
pp. 1283-1324
Author(s):  
Xi Tang ◽  
Zhaoyong Huang
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension ◽  
Semidualizing Modules

scholarly journals Homological aspects of semidualizing modules

2010 ◽  
Vol 106 (1) ◽  
pp. 5 ◽  
Author(s):  
Ryo Takahashi ◽  
Diana White
Keyword(s):  
Projective Dimension ◽  
Dual Theory ◽  
Injective Dimension ◽  
Relative Cohomology ◽  
Semidualizing Module ◽  
Finite Projective Dimension ◽  
Semidualizing Modules ◽  
The Relationship ◽  
Cohomology Modules

We investigate the notion of the $C$-projective dimension of a module, where $C$ is a semidualizing module. When $C=R$, this recovers the standard projective dimension. We show that three natural definitions of finite $C$-projective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results that demonstrate the deep connections between modules of finite projective dimension and modules of finite $C$-projective dimension. In parallel, we develop the dual theory for injective dimension and $C$-injective dimension.

Modules of finite projective dimension and cocovers

1996 ◽  
Vol 306 (1) ◽  
pp. 445-457 ◽  
Author(s):  
Dieter Happel ◽  
Luise Unger
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension

Maximally differential ideals of finite projective dimension

2021 ◽  
Vol 166 ◽  
pp. 102936
Author(s):  
Cleto B. Miranda-Neto
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension

Finite projective dimension over pullbacks of local rings

1991 ◽  
Vol 19 (12) ◽  
pp. 3271-3294 ◽  
Author(s):  
Hing Shing Man
Keyword(s):  
Projective Dimension ◽  
Local Rings ◽  
Finite Projective Dimension

The grothendieck group of the category of modules of finite projective dimension over certain weakly triangular algebras

2000 ◽  
Vol 28 (3) ◽  
pp. 1387-1404 ◽  
Author(s):  
Eduardo N. Marcos ◽  
Héctor A. Merklen ◽  
María I. Platzeck
Keyword(s):  
Grothendieck Group ◽  
Projective Dimension ◽  
Finite Projective Dimension ◽  
Category Of Modules ◽  
Triangular Algebras

Dualities for modules of finite projective dimension

2021 ◽  
pp. 61-101
Author(s):  
Birge Huisgen-Zimmermann ◽  
Manuel Saorín
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension

scholarly journals Modules of finite projective dimension with negative intersection multiplicities

1985 ◽  
Vol 79 (2) ◽  
pp. 253-291 ◽  
Author(s):  
Sankar P. Dutta ◽  
M. Hochster ◽  
J. E. McLaughlin
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension ◽  
Intersection Multiplicities

scholarly journals Torsion in kernels of induced maps on divisor class groups

2015 ◽  
Vol 14 (08) ◽  
pp. 1550123
Author(s):  
Sean Sather-Wagstaff ◽  
Sandra Spiroff
Keyword(s):  
Projective Dimension ◽  
Class Groups ◽  
Divisor Class ◽  
Finite Projective Dimension ◽  
Induced Maps

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith–Weston which applies when I is principal.

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