Search

It is well-known that idempotents lift modulo any nil one-sided ideal. While this is not true for periodic elements, it does hold true in many special cases. We investigate the connections between these special cases, as well as limitations. We also answer three questions from the literature. For example, we construct a nilpotent ideal where torsion-units lift, but periodic elements do not lift, modulo that ideal. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish a determinantal formula for matrix commutators over a commutative ring, using (among other invariants) the quantum traces of and . Special forms of this determinantal formula include a “trace version”, and a “supertrace version”. Some applications of these formulas are given to the study of value sets of binary quadratic forms, the factorization of integral matrices, and the solution of certain simultaneous diophantine equations over commutative rings. [Copyright &y& Elsevier]