Ellis begins by comparing I Tim 2:9-13 with I Cor 14:34f and I Pet 3:3-6. His purpose in doing this is twofold: 1) he wants readers to note the similarities in vocabulary and topic between these three passages, and 2) he wants readers to conclude that Paul is using a traditional "household code" in I Tim 2:9-13. The second point needs to be unpacked a bit. One of Ellis' contributions to scholarship has been his observation that Paul utilized several early church traditions in his epistles. A tradition can be understood as a hymn or statement of faith which the early church utilized in its meetings. Some of these may have been written by Paul himself, although that is not significant. Perhaps the most agreed upon traditional piece which scholars recognize is Phil 2:6-11. "Household codes" are common in the NT letters. They are exhortations given to those of the household: husbands, wives, children, slaves, and masters (e.g. Eph 5). Ellis argues that this I Tim 2 passage is a traditional piece which circulated in the early church that is also a "household code" which is primarily discussing the role of husbands and wives. What Paul has done here is to take the "household code" and juxtapose it with the church worship setting.
Based on the conclusion that these are traditional "household codes," Ellis argues that the words for "women" and "men" should be understood to be "wives" and "husbands." These are the same Greek words used in the I Cor 14:34f passage (surprise! surprise! See the second post for more details). Since their semantic range encompasses both possibilities, it is up to contextual clues to tip the scale one way or the other. Ellis notes three contextual clues to support a "wife/husband" reading: 1) the relationship of this passage with other "household codes", 2) Paul uses the illustration of Adam and Eve which points to the marriage relationship, and 3) the promise to the "observant woman, which is connected with childbirth" (Ellis, Pauline Theology, 72). This appeal to women giving birth points to the household setting and not the worship setting.
Thus, Ellis concludes that Paul does not allow a married woman to teach or exercise authority over her own husband. A single woman, however, is not limited by this and has more ministry flexibility. What is key here in understanding Ellis is that he views Paul as limiting certain women not because they are women, but only if their practice of gifts would violate the roles in marriage. In other words, Paul is very open to women exercising their gifts and assuming various roles in the church, but if their exercise of ministry causes them to violate their role in marriage, then they should limit themselves.
One final point which Ellis makes concerns the role of bishop which is discussed in I Tim 3:2. This post is in danger of being too long already, so I will just give Ellis' conclusion. Ellis notes that Paul may also exclude women from becoming bishops in the church if we understand the bishop to be a single leader of a church. Another option, which Ellis also states is valid, is that women are not excluded from this role if the leadership structure of the church has multiple leaders (i.e. multiple bishops/plurality). Once again, however, if this role causes the women to be teaching or in authority over her husband, then she would have to step down.