Reverse order laws in rings with involution.
In a ring with involution, \(a^\#\) stands for the group inverse, and \(a^\dagger\) for the Moore-Penrose inverse of \(a\). Various equivalent conditions to each of a number reverse order laws are presented. Among these laws are \((ab)^\#=b^\#(a^\dagger abb^\#)^\#a^\dagger\), \((ab)^\#=b^*(a^\#abb^*)^\#a^\#\), \((ab)^\#=b^\dagger a^\#\), \(b^\#(a^*abb^\#)^\#a^*=b^\#a^*\), \((abb^\dagger)^\#=(a^\#abb^\dagger)^\#a^\#\), and their variants. Also, sufficient conditions for each of several laws (similar to the first two above) are found.
scientific article; zbMATH DE number 6368767