Semiprime crossed products over copointed Hopf algebras

We prove a result on the transfer of essentiality of extensions of modules over subnormalizing extensions of rings, then apply it to look at the semiprimeness of Hopf-Galois extensions, in particular that of crossed products.

[1]  S. Raianu,et al.  Hopf algebras : an introduction , 2001 .

[2]  H. Schneider,et al.  Prime ideals in Hopf galois extensions , 1999 .

[3]  S. Westreich,et al.  Semiinvariants for hopf algebra actions , 1994 .

[4]  H. Schneider.  On Inner Actions of Hopf Algebras and Stabilizers of Representations , 1994 .

[5]  Susan Montgomery,et al.  Hopf algebras and their actions on rings , 1993 .

[6]  S. Montgomery,et al.  Ideals and Quotients in Crossed Products of Hopf Algebras , 1992 .

[7]  W. Chin.  Crossed products of semisimple cocommutative Hopf algebras , 1992 .

[8]  Davida Fischman,et al.  Hopf Galois extensions, smash products, and Morita equivalence , 1990 .

[9]  S. Montgomery,et al.  Crossed products and Galois extensions of Hopf algebras. , 1989 .

[10]  D. Quinn,et al.  Rings graded by polycyclic-by-finite groups , 1988 .

[11]  S. Montgomery,et al.  Addendum to: “Group-graded rings, smash products, and group actions” [Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258; MR0728711 (85i:16002)] , 1987 .

[12]  E. A. Whelan.  Finite subnormalizing extensions of rings , 1986 .

[13]  D. Quinn.  Group-graded rings and duality , 1985 .

[14]  S. Montgomery,et al.  Group-graded rings, smash products, and group actions , 1984 .

[15]  B. Lemonnier.  Dimension de krull et dualite de morita dans les extensions triangulaires , 1984 .

[16]  D. Passman.  It's essentially Maschke's theorem , 1983 .

[17]  L. Rowen,et al.  Group graded rings , 1983 .

[18]  C. Nastasescu,et al.  Graded ring theory , 1982 .

[19]  S. Montgomery,et al.  Semiprime Skew Group Rings , 1978 .