Evaluations of Polynomials in Algebras: Images, Identities, Gradings and Connectio...
Grant number: | 16/07173-6 |
Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
Start date: | June 01, 2016 |
End date: | December 31, 2017 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
Principal Investigator: | Humberto Luiz Talpo |
Grantee: | Fernando Sônego de Toledo |
Host Institution: | Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil |
Abstract The algebras that satisfy polynomial identities (so-called PI-algebras) form an important class of algebras, and therefore they have been attracting the attention of the algebraist. A polynomial identity of an algebra A is a polynomial f(x1,...,xn) in noncommutative variables such that f(a1,...,an)=0 in A for all a1,...,an in A. If there exist f(x1,...,xn) nonzero we say that A is a PI-algebra. Some examples of PI-algebras: Commutative algebras, finite dimensional algebras and nilpotent algebras. In this work we will study some algebras with polynomial identities, in particular the matrix algebra. | |
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