Automorphic-differential identities

and actions of pointed coalgebras on rings

Author:
Tadashi Yanai

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let be a ring, its left Martindale quotient ring and a right ideal of having no nonzero left annihilator. (1) Let be a pointed coalgebra which measures such that the group-like elements of act as automorphisms of . If is prime and for , then . Furthermore, if the action of extends to and if such that , then . (2) Let be an endomorphism of given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If is semiprime and , then .

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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

DOI:
https://doi.org/10.1090/S0002-9939-98-04479-7

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

Article copyright:
© Copyright 1998
American Mathematical Society