This is a messy section that has given scholars a headache for centuries. Other resources (in addition to those mentioned by Sandra):

1. Because different manuscripts list these verses in different places, some scholars argue that the verses were a later addition (a common explanation when that's the problem)--G. D. Fee, First Corinthians [NICNT], 697-710; P. B. Payne, “Fuldensis, Sigla for Variants in Vaticanus, and 1 Cor 14.34-5,” NTS 41 [1995]: 240-262. I believe the verses to be original, although the fact that they're shifted around by early scribes and written in margins in some places show the difficulty even the early church had with this passage.

2. Many scholars hold to the view that this passage talks about women speaking against, or judging, the prophets in this situation (rather than the women not speaking in church period, which would go against 1 Corinthians 11, a passage that talks about women prophesying in church--and it's interesting to note that Paul never specifies that they prophesy to other women only)--Bruce, 1 and 2 Corinthians, pp. 136-37; Morris, pp. 201-2; Robertson and Plummer, p. 325; James B. Hurley, Man and Woman In Biblical Perspective, pp. 188, 190; Thomas Constable, http://soniclight.com/constable/notes/pdf/1corinthians.pdf, and the NET Bible (see notes for 1 Corinthians 14:33-36).

Corollary: Some scholars, such as G. Campbell Morgan, believe that Paul wrote the prohibition in ch. 14 because of conditions unique in Corinth. For example, the passage implies that Paul addressed a specific situation in which chaos rather than order ruled the church worship service (the overall problem Paul addresses in ch. 14), and this disruption discouraged the strengthening and encouragement for which the service was intended. The book Sandra mentions explains a unique situation in Rome concerning the "new" woman v. the "old" woman Caesar wished to re-establish with dress codes and other "proper" behavior.

Within these, an idea exists of protecting respectable relations between men and women within the culture in order to strengthen the church. This leads me back to my original question: how can we in today's culture create relations between men and women that encourage respect for the strengthening of the church (especially when affairs lead to the detoriation of the local churches)?