TY - JOUR

T1 - Corrigendum to "Morita theory for coring extensions and cleft bicomodules" [Adv. Math. 209 (2) (2007) 611-648] (DOI:10.1016/j.aim.2006.05.010)

AU - Böhm, Gabriella

AU - Vercruysse, Joost

PY - 2009/6/1

Y1 - 2009/6/1

N2 - The results in our paper heavily rely on the journal version of [T. Brzeziński, A note on coring extensions, Ann. Univ. Ferrara Sez. VII (N.S.) 51 (2005) 15-27; a corrected version is available at http://arxiv.org/abs/math/0410020v3, Theorem 2.6]. Since it turned out recently that in the proof of the quoted theorem there are some assumptions missing, our derived results are not expected to hold at the stated level of generality either. Here we supplement the constructions in our article with the missing assumptions and show that they hold in most of our examples. In order to handle also the non-fitting case of cleft extensions by arbitrary Hopf algebroids, Morita contexts are constructed that do not necessarily correspond to coring extensions. They are used to prove a Strong Structure Theorem for cleft extensions by arbitrary Hopf algebroids. In this way we obtain in particular a corrected form of the journal version of [G. Böhm, Integral theory for Hopf algebroids, Algebr. Represent. Theory 8 (4) (2005) 563-599; Corrigendum, to be published; see also http://arxiv.org/abs/math/0403195v4, Theorem 4.2], whose original proof contains a similar error.

AB - The results in our paper heavily rely on the journal version of [T. Brzeziński, A note on coring extensions, Ann. Univ. Ferrara Sez. VII (N.S.) 51 (2005) 15-27; a corrected version is available at http://arxiv.org/abs/math/0410020v3, Theorem 2.6]. Since it turned out recently that in the proof of the quoted theorem there are some assumptions missing, our derived results are not expected to hold at the stated level of generality either. Here we supplement the constructions in our article with the missing assumptions and show that they hold in most of our examples. In order to handle also the non-fitting case of cleft extensions by arbitrary Hopf algebroids, Morita contexts are constructed that do not necessarily correspond to coring extensions. They are used to prove a Strong Structure Theorem for cleft extensions by arbitrary Hopf algebroids. In this way we obtain in particular a corrected form of the journal version of [G. Böhm, Integral theory for Hopf algebroids, Algebr. Represent. Theory 8 (4) (2005) 563-599; Corrigendum, to be published; see also http://arxiv.org/abs/math/0403195v4, Theorem 4.2], whose original proof contains a similar error.

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U2 - 10.1016/j.aim.2008.11.018

DO - 10.1016/j.aim.2008.11.018

M3 - Comment/debate

AN - SCOPUS:63049126038

VL - 221

SP - 682

EP - 686

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -