Algebra Commons^™

Combinatorial Polynomial Identity Theory, Mayada Khalil Shahada

Electronic Thesis and Dissertation Repository

This dissertation consists of two parts. Part I examines certain Burnside-type conditions on the multiplicative semigroup of an (associative unital) algebra $A$.

A semigroup $S$ is called $n$-collapsing if, for every $a_1,\ldots, a_n \in S$, there exist functions $f\neq g$ on the set $\{1,2,\ldots,n\}$ such that \begin{center} $s_{f(1)}\cdots s_{f(n)} = s_{g(1)}\cdots s_{g(n)}$. \end{center} If $f$ and $g$ can be chosen independently of the choice of $s_1,\ldots,s_n$, then $S$ satisfies a semigroup identity. A semigroup $S$ is called $n$-rewritable if $f$ and $g$ can be taken to be permutations. Semple and Shalev extended Zelmanov's Fields Medal writing solution of the Restricted …