Automorphic-differential identities and actions of pointed coalgebras on rings
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- by Tadashi Yanai PDF
- Proc. Amer. Math. Soc. 126 (1998), 2221-2228 Request permission
Abstract:
In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let $R$ be a ring, $R _{\mathcal {F}}$ its left Martindale quotient ring and $\mathfrak {A}$ a right ideal of $R$ having no nonzero left annihilator. (1) Let $C$ be a pointed coalgebra which measures $R$ such that the group-like elements of $C$ act as automorphisms of $R$. If $R$ is prime and $\xi \cdot \mathfrak {A}=0$ for $\xi \in R\#C$, then $\xi \cdot R=0$. Furthermore, if the action of $C$ extends to $R _{\mathcal {F}}$ and if $\xi \in R _{\mathcal {F}}\#C$ such that $\xi \cdot \mathfrak {A}=0$, then $\xi \cdot R _{\mathcal {F}}=0$. (2) Let $f$ be an endomorphism of $R _{\mathcal {F}}$ given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If $R$ is semiprime and $f(\mathfrak {A})=0$, then $f(R)=0$.References
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Additional Information
- Tadashi Yanai
- Affiliation: Department of Mathematics, Niihama National College of Technology, 7-1 Yagumo-cho, Niihama, Ehime, 792, Japan
- Email: yanai@sci.niihama-nct.ac.jp
- Received by editor(s): May 31, 1996
- Received by editor(s) in revised form: October 24, 1996, and January 24, 1997
- Communicated by: Ken Goodearl
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2221-2228
- MSC (1991): Primary 16W20, 16W25, 16W30
- DOI: https://doi.org/10.1090/S0002-9939-98-04479-7
- MathSciNet review: 1459157