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Homological aspects of the dual Auslander transpose
-
Xi Tang
and
Zhaoyong Huang
Published/Copyright:
September 9, 2014
Abstract
As a dual of the Auslander transpose of modules, we introduce and study the cotranspose of modules with respect to a semidualizing module C. Then using it we introduce n-C-cotorsionfree modules, and show that n-C-cotorsionfree modules possess many dual properties of n-torsionfree modules. In particular, we show that n-C-cotorsionfree modules are useful in characterizing the Bass class and investigating the approximation theory for modules. Moreover, we study n-cotorsionfree modules over Artin algebras and answer negatively an open question of Huang and Huang posed in 2012.
Keywords: Cotranspose; n-C-cotorsionfree modules; n-C-cospherical modules; n-syzygy modules; cograde
Funding source: NSFC
Award Identifier / Grant number: 11171142
Funding source: Mathematical Tianyuan Fund of NSFC
Award Identifier / Grant number: 11226058
Funding source: NSF of Guangxi Province of China
Award Identifier / Grant number: 2013GXNSFBA019005
Received: 2013-12-8
Published Online: 2014-9-9
Published in Print: 2015-11-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Conjugacy classes of finite groups and graph regularity
- A note about complexity of lens spaces
- A note for alternating Ramanujan's circular summation formula
- On a question of Gillespie
- Jumping pairs of Steiner bundles
- On the recurrence of symmetric jump processes
- R-groups, elliptic representations, and parameters for GSpin groups
- The least common multiple of consecutive quadratic progression terms
- Hybrid bounds for quadratic Weyl sums and arithmetic applications
- Invariants of coinvariant algebras
- Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
- Distinction of the Steinberg representation II: An equality of characters
- Perturbations of functional inequalities for Lévy type Dirichlet forms
- Decomposable Leavitt path algebras for arbitrary graphs
- Group rings whose set of symmetric elements is Lie metabelian
- Heat kernel and Lipschitz–Besov spaces
- A case of monoidal uniqueness of algebraic models
- Schur tensor product of operator spaces
- On the upper bound for Bi(K)Bi(K*)
- Bredon cohomological dimensions for proper actions and Mackey functors
- Action of the Cremona group on foliations on ℙℂ2: Some curious facts
- Homological aspects of the dual Auslander transpose
- Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
- Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
Keywords for this article
Cotranspose;
n-C-cotorsionfree modules;
n-C-cospherical modules;
n-syzygy modules;
cograde
Articles in the same Issue
- Frontmatter
- Conjugacy classes of finite groups and graph regularity
- A note about complexity of lens spaces
- A note for alternating Ramanujan's circular summation formula
- On a question of Gillespie
- Jumping pairs of Steiner bundles
- On the recurrence of symmetric jump processes
- R-groups, elliptic representations, and parameters for GSpin groups
- The least common multiple of consecutive quadratic progression terms
- Hybrid bounds for quadratic Weyl sums and arithmetic applications
- Invariants of coinvariant algebras
- Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
- Distinction of the Steinberg representation II: An equality of characters
- Perturbations of functional inequalities for Lévy type Dirichlet forms
- Decomposable Leavitt path algebras for arbitrary graphs
- Group rings whose set of symmetric elements is Lie metabelian
- Heat kernel and Lipschitz–Besov spaces
- A case of monoidal uniqueness of algebraic models
- Schur tensor product of operator spaces
- On the upper bound for Bi(K)Bi(K*)
- Bredon cohomological dimensions for proper actions and Mackey functors
- Action of the Cremona group on foliations on ℙℂ2: Some curious facts
- Homological aspects of the dual Auslander transpose
- Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
- Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
