So you don't have any hard and fast rules as to what that management looks like and yet you say that in Jewish culture ONLY the husband managed the household. So it would seem that you do have some vision as to what that means in Jewish culture.
Well, whatever definition we come up with, it's got to take Proverbs 31 into account. That woman was managing her household.
It also has to take Romans 16 into account--the issue of Phoebe. She is most probably the leader of the delegation that carried Paul's letter to the Romans, Paul calls her a "deacon," and further instructs the Roman Christians to help her further in
her business.
I think both situations fall under the military example I provided earlier.
Someone up above--it was probably Episaw, made the connection of "authority" with eldership. I suspect there are several distinctions of those terms to be made with regard to how Paul thought of them as he instructed the congregation.
First--to cut to the chase--Paul's connection of eldership and teaching both involved
disciplinary authority. Elders held disciplinary authority over the congregation, teachers held disciplinary authority over their disciples. I believe that is the distinction in Paul's head--that women should not have
disciplinary authority over men.
There are a lot of ways and roles in which someone might be a "deacon" or a "pastor" without having disciplinary authority, particularly when we understand the military example I gave: When the commander of all the troops places one in authority over another saying, "Obey
him or you will answer to
me." The commander delegates task-limited instructional authority but retains disciplinary authority to himself.
Sometimes we do the same. A woman may be put in charge of the church nursery. In most cases, she would have the authority to tell any adult--including men--to leave the room if they seem to be hanging around unnecessarily--that's task-instructional authority. If the man resisted, however, she does not have the authority to discipline him. If discipline is going to be done, it will be by elders or some other party.
In Paul's time, a teacher had disciplinary authority over his disciples. Paul would not have allowed a woman to have that kind of authority over a man, but he didn't see a problem with Priscilla expounding the gospel to Apollos--there was no question of disciplinary authority involved.
Nor would there have been a problem with Phoebe being a deacon given the task of transporting Paul's letter to the Romans, even if she were directing the men who accompanied her (which there would have been--she would not have been making that trip alone). That would have been task-instructional authority, not disciplinary authority.