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- Title
FULLY BOUNDED NOETHERIAN RINGS AND FROBENIUS EXTENSIONS.
- Authors
CAENEPEEL, S.; GUÉDÉNON, T.
- Abstract
Let i: A → R be a ring morphism, and χ: R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1R) = 1A. If R is a Frobenius A-ring, then we can define a trace map tr: A → AR. If there exists an element of trace 1 in A, then A is right FBN if and only if AR is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover results of García and del Río, and Dǎscǎlescu, Kelarev and Torrecillas on actions of group and Hopf algebras on FBN rings as special cases. We also obtain applications to extensions of Frobenius algebras, and to Frobenius corings with a grouplike element.
- Subjects
NOETHERIAN rings; FROBENIUS algebras; RING extensions (Algebra); MORPHISMS (Mathematics); HOPF algebras
- Publication
Journal of Algebra & Its Applications, 2007, Vol 6, Issue 2, p189
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498807002107