Non-PRO Japanese to English Art/Literary Cinema, Film, TV, Drama

Dear ProZ members,

could you help me to understand the meaning of 極道渡世? 極道 stands for yakuza, of course, but what about 渡世? "Tha yakuza trade", "the yakuza business"?

I'm finding it in the following senteces from a cartoon. They are said by yakuza members willing to help their clan.

全ては組のため、極道渡世のため！
(Everything is for the clan, for the yakuza business!)

明日からまた、極道渡世のために仁義の通った仕事、頑張って行きます
(From tomorrow, we'll do our best again to do moral works for the yakuza business!)

(I suppose that 仁義の通った仕事 stands for "works permeated by morality" or something like that.)

Thank you for your help!