Automatic surjectivity of ring homomorphisms on -algebras and algebraic differences among some group algebras of compact groups

Author:
Lajos Molnár

Journal:
Proc. Amer. Math. Soc. **128** (2000), 125-134

MSC (1991):
Primary 46K15, 47D50, 47B49; Secondary 43A15, 43A22

DOI:
https://doi.org/10.1090/S0002-9939-99-04974-6

Published electronically:
June 30, 1999

MathSciNet review:
1616645

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Abstract: In this paper we present two automatic surjectivity results concerning ring homomorphisms between -classes of an -algebra which, in some sense, improve the main theorem in a recent paper by the author (*Proc. Amer. Math. Soc.* **124** (1996), 169-175) quite significantly. Furthermore, we apply our results to show that for arbitrary infinite compact groups , no quotient ring of is isomorphic to , a statement we conjecture to be true for every pair of group rings corresponding to different exponents .

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Additional Information

**Lajos Molnár**

Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P. O. Box 12, Hungary

Email:
molnarl@math.klte.hu

DOI:
https://doi.org/10.1090/S0002-9939-99-04974-6

Keywords:
Ring homomorphism,
$H^{*}$-algebra,
$p$-class,
compact group,
group algebra,
automatic surjectivity

Received by editor(s):
March 4, 1997

Received by editor(s) in revised form:
March 10, 1998

Published electronically:
June 30, 1999

Additional Notes:
This paper was completed when the author, holding a Hungarian State Eötvös Scholarship, was a visitor at the University of Maribor, Slovenia. This research was supported also by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T–016846 F–019322.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society