A commuting-( b , c )-polar element in semigroups
Taohua Jin, Xavier Mary, Huihui Zhu · Communications in Algebra · 2025
Given any semigroup S, a,b,c∈S and j=1,2, the element a is called commj-(b,c)-polar if there exists some p∈S such that p2=p∈commj(a), pb=b, cp=c and p∈abSca. A list of criteria and characterizations of the commj-(b,c)-polarity are established. We show that an element a is commj-(b,c)-polar if and only if it is commj-(b,c)-invertible in the sense of Drazin. A detailed study is carried out on Cline’s property and the absorption law of commj-(b,c)-polar elements, and on the connection between commj-(b,c)-polarity and some other generalized inverses.