Mikvaos, Chapter 8, Mishnah 4. Our Mishnah presents a basic rule about the tumah of shichvas zera: only that of a Jewish man carries tumah, while that of a non-Jew is entirely free of tumah. The Mishnah demonstrates the rule from two opposite angles, and then appends two practical situations in which an immersion turns out to be worthless because of a preparation the person neglected beforehand.
The Non-Jewish Woman and the Jewish Woman
"Ovedes kochavim shepoletes shichvas zera miYisroel, temeiah." A non-Jewish woman who was intimate with a Jew, and whose body afterward expelled that shichvas zera while it is still regarded as potent (the period defined in the previous mishnah), becomes temeiah. She herself stands outside the framework of tumah and taharah as it ordinarily applies, yet what emerged from her originated in a Jew, and the shichvas zera of a Jewish man is mitameh by touch.
Here a distinction is worth noting. Her own tumah in this case is only miderabbanan. Anyone else, however, who comes into contact with that shichvas zera contracts tumah on the level of de'oraisa, because the substance itself carries genuine Torah tumah.
The opposite situation produces the opposite halachah. "Bas Yisroel shepoletes shichvas zera me'oved kochavim, tehorah." A Jewish woman who was intimate with a non-Jew, and whose body subsequently expelled that shichvas zera, remains tehorah, even during the stretch of time in which such a discharge would otherwise still count as potent. The explanation is simple: the shichvas zera of a non-Jew possesses no tumah whatsoever, so there is nothing here capable of conveying tumah.
Toveling Without Cleaning First
"Ha'isha sheshimshah beisah veyardah vetavlah velo kibdah es habayis, ke'ilu lo tavlah." A woman who had relations and then went down and immersed without first cleaning herself of any residue that may have remained in her body: her tevilah accomplishes nothing, and she is treated as though she had never immersed at all. The concern is that she may afterward discharge that shichvas zera, and it will render her tamei once again, through contact and through carrying. Since the cause of the tumah was present in her body at the moment of the tevilah, the immersion cannot be relied upon.
The Ba'al Keri Who Did Not Urinate
"Ba'al keri shetaval velo hitil es hamayim, kesheyatil es hamayim, tamei." A man who experienced a keri and immersed, but did not urinate before his tevilah, becomes tamei when he later urinates. The reason is the concern that traces of keri remained within him, and that when he urinates they will be carried out and render him tamei through contact with shichvas zera. This tumah is only miderabbanan, and it is relevant only with regard to terumah.
"Rebbi Yosi omeir: becholeh uvezakein, tamei; beyeled uvebari, tahor." Rebbi Yosi limits the ruling. In the case of a man who is ill or elderly, we do indeed suspect that not everything was expelled, and he is tamei. But in the case of a young, healthy and vigorous man, we assume that the discharge came out with full force and that no residue was left behind, and therefore he remains tahor.