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The automatic continuity for particular type of homomorphism nonassociative algebras | ||
| Journal of Education and Science | ||
| Article 21, Volume 21, Issue 3, 2008, Pages 153-159 PDF (0 K) | ||
| DOI: 10.33899/edusj.2008.56038 | ||
| Authors | ||
| Roqya Ballo; Amer Mohammed | ||
| Abstract | ||
| Abstract Rodriguez conjecture ensures the automatic continuity of a dense range homomorphism from a complete normed nonassociative algebra into another one with zero strong radical. Rodriguez conjecture still unsolved. But there is an affirmative answer of Rodriguez conjecture presented by Rodriguez himself in [7] for particular type of nonassociative algebras called power-associative algebra. Also the authors in [11] gived an approximate solution of Rodriguez conjecture by putting a condition on multiplication algebra of a domain of such homomorphism. In this work, we give another partial solution of Rodriguez conjecture as follows: If A and B are complete normed nonassociative algebras and if is a dense range homomorphism from A into B such that B simple with identity and multiplication algebra of B is also simple. Then is continuous. | ||
| Keywords | ||
| homomorphism; nonassociative algebra; automatic continuity | ||
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