Abstract
Let H be a Hopf algebra over a field \(\mathbbm {k}\). In this paper we present a general theory on partial H-radicals in the sense of Amitsur-Kurosh, for partial H-module algebras, as made in Fisher (J Algebra 34:217–231, 1975) and Sidorov (Algebra i Logika 28(6):705–721, 1989) for global actions, and study some partial H-radicals of Jacobson type. Among other results we discuss some questions posed by Fisher (1975) in the context of partial actions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abadie, F., Dokuchaev, M., Exel, R., Simón, J.J.: Morita equivalence of partial group actions and globalization. http://mtm.ufsc.br/exel/papers/moritaglob.pdf (2011)
Alves, M.M.S., Batista, E.: Partial Hopf actions, partial invariants and a Morita context. Algebra Discrete Math. 3, 1–19 (2009)
Alves, M.M.S., Batista, E., Verruysse, J.: Partial representation of Hopf algebras. J. Algebra 426, 137–187 (2015)
Anderson, T., Divinsky, N., Suliński, A.: Hereditary radicals in associative and alternative rings. Can. J. Math. 17, 594–603 (1965)
Caenepeel, S., Janssen, K.: Partial (co)actions of Hopf algebras and partial Hopf-Galois theory. Commun. Algebra 36, 2923–2946 (2008)
Cavalheiro, R.: Sobre a semiprimitividade e a semiprimalidade do produto smash parcial. Ph.D. thesis, Universidade Federal do Rio Grande do Sul, Brasil (2013) (in Portuguese)
Dokuchaev, M., Exel, R.: Associativity of crossed products by partial actions, enveloping actions and partial representations. Trans. Am. Math. Soc. 357(5), 1931–1952 (2005)
Dokuchaev, M., Ferrero, M., Paques, A.: Partial actions and Galois theory. J. Pure Appl. Algebra 208, 77–87 (2007)
Exel, R.: Circle actions on \({C}^{\star }\)-algebras, partial automorphisms and generalized Pimsner-Voiculescu exact sequences. J. Funct. Anal. 122(3), 361–401 (1994)
Fisher, J.R.: A Jacobson radical for Hopf module algebras. J. Algebra 34, 217–231 (1975)
Gardner, B.J., Wiegandt, R.: Radical Theory of Rings, Volume 261 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York (2004)
Montgomery, S., Schneider, H.J.: Prime ideals in Hopf Galois extensions. Isr. J. Math. 112, 187–235 (1999)
Sidorov, A.V.: Radicals of H-module algebras. Algebra i Logika 28(6), 705–721 (1989)
Zhang, S.: Braided Hopf algebras. arXiv:math/0511251v10 [math.RA] (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by PNPD Program - CAPES, Brazil.
Rights and permissions
About this article
Cite this article
Cavalheiro, R., Sant’Ana, A. On partial H-radicals of Jacobson type. São Paulo J. Math. Sci. 10, 140–163 (2016). https://doi.org/10.1007/s40863-015-0036-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40863-015-0036-y