1. Conjectures for the existence of an idempotent in $\omega $-polynomial algebras
- Author
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Michelle Nourigat and Richard Varro
- Subjects
Polynomial ,Pure mathematics ,Identity (mathematics) ,Conjecture ,Applied Mathematics ,Idempotence ,Discrete Mathematics and Combinatorics ,Idempotent element ,Algebra over a field ,Double root ,Omega ,Analysis ,Mathematics - Abstract
The existence of idempotent elements in baric algebras defined by $\omega$-polynomial identities ($\omega$-PI algebras) is an important problem for the study of genetic algebras. We conjecture here two criteria on the existence of an idempotent. These criteria are based on the existence of 1/2 as double root of a polynomial built from the identity defining a $\omega$-PI algebra. We show that these criteria are true in all the algebras studied until now and for which we have results concerning the existence of idempotent elements.
- Published
- 2011
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