[图书][B] Corings and comodules
T Brzezinski, R Wisbauer - 2003 - books.google.com
This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …
part, the module-theoretic aspects of coalgebras over commutative rings are described …
Homological aspects of the dual Auslander transpose, II
X Tang, Z Huang - 2017 - projecteuclid.org
Let R and S be rings, and let R ω S be a semidualizing bimodule. We prove that there exists
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …
Adjoint functors and equivalences of subcategories
FC Iglesias, J Gómez-Torrecillas, R Wisbauer - Bulletin des sciences …, 2003 - Elsevier
For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …
On Galois comodules
R Wisbauer - Communications in Algebra®, 2006 - Taylor & Francis
Generalizing the notion of Galois corings, Galois comodules were introduced as comodules
P over an A-coring 𝒞 for which PA is finitely generated and projective and the evaluation …
P over an A-coring 𝒞 for which PA is finitely generated and projective and the evaluation …
Baer-Kaplansky classes in categories: transfer via functors
S Crivei, DK Tütüncü, R Tribak - Communications in Algebra, 2020 - Taylor & Francis
We study the transfer of Baer-Kaplansky classes via additive functors between preadditive
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …
On Galois corings
R Wisbauer - Hopf algebras in noncommutative geometry and …, 2019 - taylorfrancis.com
For a long period the theory of modules over rings on the one hand and comodules and
Hopf modules for coalgebras and bialgebras on the other side developed quite …
Hopf modules for coalgebras and bialgebras on the other side developed quite …
Idempotent monads and⋆-functors
J Clark, R Wisbauer - Journal of Pure and Applied Algebra, 2011 - Elsevier
For an associative ring R, let P be an R-module with S= EndR (P). C. Menini and A. Orsatti
posed the question of when the related functor HomR (P,−)(with left adjoint P⊗ S−) induces …
posed the question of when the related functor HomR (P,−)(with left adjoint P⊗ S−) induces …
Duality pairs induced by Auslander and Bass classes
Z Huang - Georgian Mathematical Journal, 2021 - degruyter.com
Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C(R op)
and ℬ C(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C(R …
and ℬ C(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C(R …
[HTML][HTML] On faithfully balanced modules, F-cotilting and F-Auslander algebras
B Ma, J Sauter - Journal of Algebra, 2020 - Elsevier
The aim of this paper is to give a unification of the theory of (co) tilting modules and (higher)
Auslander correspondence by using faithfully balanced modules (ie, faithful modules with …
Auslander correspondence by using faithfully balanced modules (ie, faithful modules with …
QF functors and (co) monads
B Mesablishvili, R Wisbauer - Journal of Algebra, 2013 - Elsevier
One reason for the universal interest in Frobenius algebras is that their characterisation can
be formulated in arbitrary categories: a functor K: A→ B between categories is Frobenius if …
be formulated in arbitrary categories: a functor K: A→ B between categories is Frobenius if …