Sotah, Chapter Four, Mishnah One
Our mishnah deals with situations in which the woman, suspected of committing adultery, does not have the opportunity to drink the bitter waters, but rather she must be divorced and does not receive her ketubah.
1) A betrothed woman and a shomeret yavam do not drink [the bitter waters] and do not receive their ketubah, as it is said, When a wife, being under her husband, goes astray (Numbers 5:29), this excludes a betrothed woman and a shomeret yavam.
2) A widow who had married a high priest, a divorced woman or a halutzah who had married an ordinary priest, a mamzeret or a netinah who had married an Israelite, and the daughter of an Israelite who had married a mamzer or a natin do not drink [the bitter waters] and do not receive their ketubah.
Section one: The Torah uses the word wife (alternatively translated as woman) in summarizing the laws of the Sotah. From here the rabbis deduce that she must have the status of full wife in order to drink the bitter waters. A betrothed woman does not have such a status and hence, even if her fiancé forbids her from being secluded with a certain man and afterwards she is secluded with him, she does not undergo the sotah ordeal. Similarly, a shomeret yavam, a woman whose husband died childless and is waiting for either levirate marriage (yibbum) or the release from levirate marriage (halitzah), does not drink the bitter waters. This refers to a case where the yavam, her brother-in-law, warned her not to be secluded with a certain man.
Both of these women do lose their ketubah, since they were secluded after being warned; however, neither is allowed to undergo the sotah ordeal.
Section two: This section is also based on the fact that the Torah uses the word wife. Here wife excludes a woman who was prohibited from being her husbands wife. The mishnah lists all relations which are prohibited and yet nevertheless the marriage is legally valid (the marriage would not be valid in cases of incest). This includes the widow who may not marry the high priest, and the divorcee and halutzah (woman who had previously been released from levirate marriage) who may not marry a normal priest. With regard to Israelites it includes the prohibition of marrying a mamzer (one born of forbidden sexual union) and natin (descendent of Temple slaves). We have already encountered these categories in various places in Yevamot and Ketubot.
We should note that according to the Rambam, the waters dont work in these cases because the husband married a woman forbidden to him. The waters work only when the husband is also free from having committed any transgressions.