On partial H-radicals of Jacobson type
Tóm tắt
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.
Tài liệu tham khảo
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)