The reverse order law of the $(b,c)$-inverse in rings

Abstract

We present equivalent conditions of reverse order law for the $(b,c)$-inverse $(aw{)}^{(b,c)}=w^{(b,s)}{a}^{(t,c)}$ to hold in a ring. Also, we study various mixed-type reverse order laws for the $(b,c)$-inverse. As a consequence, we get results related to the reverse order law for the inverse along an element. More general case of reverse order law $(a_1{a}_2{)}^{(b_3,c_3)}=a_2^{(b_2,c_2)}{a}_1^{(b_1,c_1)}$ is considered too.

References in corpus (1)

• Characterizations of the $(b,c)$-inverse in a ring