Annihilators, multipliers and crossed modules (Q1417763)

Actor squares for a crossed module of groups were introduced by \textit{K. Norrie} [Bull. Soc. Math. Fr. 118, 129--146 (1990; Zbl 0719.20018)] as an analogue of automorphism groups. Like many of the concepts and tools of group based crossed module theory, the actor square can be generalised to various other types of crossed module. In this paper the authors look at the analogue for commutative algebras. Actor squares are defined and their basic theory is developed. The link between these new ideas and more classical invariants is examined. The concepts of annihilators and multipliers are extended in a useful way to crossed modules of algebras. Some applications are given.