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In the sequel, "$k$-algebra" means "associative unital finite dimensional $k$-algebra. Apologies for the very long exposition. If $A$ is a $k$-algebra and $s:A\to k$ is $k$-linear, we say that $s$ ...

Are there some books or papers about the general definition of traces: If $\mathscr{A}$ is an associative algebra over $K$ then the space of traces is the set of all linear functionals $\tau:\mathscr{...

Let $k$ be a field and $A$ a $k$-algebra with unit. The trace module is $$ T(A)=A/[A,A], $$ where $[A,A]$ is the left $A$-module generated by all elements of the form $ab-ba$ for $a,b\in A$. The ...