Injective objects of monomorphism categories
Keyan SONG, Yuehui ZHANG
Injective objects of monomorphism categories
For an acyclic quiver Q and a finite-dimensional algebra A, we give a unified form of the indecomposable injective objects in the monomorphism category Mon(Q,A) and prove that Mon(Q,A) has enough injective objects.
Monomorphism categories / injective objects
[1] |
Birkhoff G. Subgroups of abelian groups. Proc Lond Math Soc II, 1934, 38(2): 385–401
|
[2] |
Chen Xiaowu. The stable monomorphism category of a Frobenius category. Math Res Lett, 2011, 18(1): 125–137
CrossRef
Google scholar
|
[3] |
Chen Xiaowu. Three results on Frobenius categories. Math Z, 2012, 270(1-2): 43–58
CrossRef
Google scholar
|
[4] |
Kussin D, Lenzing H, Meltzer H. Nilpotent operators and weighted projective lines. J Reine Angew Math, 2010, 685(6): 33–71
|
[5] |
Kussin D, Lenzing H, Meltzer H. Triangle singularities, ADE-chains, and weighted projective lines. Adv Math, 2013, 237: 194–251
CrossRef
Google scholar
|
[6] |
Luo X, Zhang P. Monic representations and Gorenstein-projective modules. Pacific J Math, 2013, 264(1): 163–194
CrossRef
Google scholar
|
[7] |
Moore A. The Auslander and Ringel-Tachikawa theorem for submodule embeddings. Comm Algebra, 2010, 38: 3805–3820
CrossRef
Google scholar
|
[8] |
Ringel C M, Schmidmeier M. Submodule categories of wild representation type. J Pure Appl Algebra, 2006, 205(2): 412–422
CrossRef
Google scholar
|
[9] |
Ringel C M, Schmidmeier M. The Auslander-Reiten translation in submodule categories. Trans Amer Math Soc, 2008, 360(2): 691–716
CrossRef
Google scholar
|
[10] |
Ringel CM, Schmidmeier M. Invariant subspaces of nilpotent operators I. J Rein Angew Math, 2008, 614: 1–52
|
[11] |
Simson D. Representation types of the category of subprojective representations of a finite poset over K[t]/(tm) and a solution of a Birkhoff type problem. J Algebra, 2007, 311: 1–30
CrossRef
Google scholar
|
[12] |
Simson D. Tame-wild dichotomy of Birkhoff type problems for nilpotent linear operators. J Algebra, 2015, 424: 254–293
CrossRef
Google scholar
|
[13] |
Song K, Kong F, Zhang P. Monomorphism operator and perpendicular operator. Comm Algebra, 2014, 42(9): 3708–3723
CrossRef
Google scholar
|
[14] |
Xiong B, Zhang P, Zhang Y. Auslander-Reiten translations in monomorphism categories. Forum Math, 2014, 26: 863–912
CrossRef
Google scholar
|
[15] |
Zhang Pu. Monomorphism categories, cotilting theory, and Gorenstein-projective modules. J Algebra, 2011, 339: 180–202
|
/
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