Slike nekomutativnih polinomov : delo diplomskega seminarja

Vitas, Daniel (author), Brešar, Matej (mentor)

Naj bo $f(X_1, \ldots, X_n)$ neničeln multilinearen nekomutativen polinom. Če je $A$ enotska algebra s surjektivnim notranjim odvajanjem, lahko vsak element iz $A$ zapišemo kot $f(a_1, \ldots, a_n)$ za neke $a_i \in A$.

• Language: Slovenian
• Keywords: multilinearen nekomutativen polinom, surjektivno notranje odvajanje, L'vov-Kaplanskyjeva domneva
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-119935
• UDC: 512.622
• COBISS.SI-ID: 58831363
• Publication date in RUL: 13.09.2020

Secondary language

• Language: English
• Title: Images of noncommutative polynomials

Abstract

Let $f(X_1, \ldots, X_n)$ be a nonzero multilinear noncommutative polynomial. If $A$ is a unital algebra with a surjective inner derivation, then every element in $A$ can be written as $f(a_1, \ldots, a_n)$ for some $a_i \in A$.

• Keywords: multilinear noncommutative polynomial, surjective inner derivation, L'vov-Kaplansky conjecture