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We present equivalent conditions of reverse order law for the (b, c)-inverse $${(a_1a_2)^{(b, c)}=a_2^{(b, s)}a_1^{(t, c)}}$$(a1a2)(b,c)=a2(b,s)a1(t,c) to hold in a semigroup. Also, we study various mixed-type reverse order laws for… Click to show full abstract
We present equivalent conditions of reverse order law for the (b, c)-inverse $${(a_1a_2)^{(b, c)}=a_2^{(b, s)}a_1^{(t, c)}}$$(a1a2)(b,c)=a2(b,s)a1(t,c) to hold in a semigroup. 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, precisely the rule $${(a_1a_2)^{(b_3, c_3)}=a_2^{(b_2,c_2)}a_1^{(b_1, c_1)}}$$(a1a2)(b3,c3)=a2(b2,c2)a1(b1,c1) is considered too.
Journal Title: Acta Mathematica Hungarica
Year Published: 2017
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