It should be noted that Beth Shammai disputed even Shammai himself and so should not be taken as the opinion of Shammai, but rather the result of Shammai's opinions. Beth Shammai Halakhah rejects the idea of salvation for non-Jews. This is usualy called "Shammai's Ruler" which contrasts with "Hillel's Golden Rule". Beth Shammai Halakhah was recorded in the Talmud through the opinions of Rabbi Eliezer. According to Beth Shammai Halakhah, Noahism should be nothing but the first step on the path of full conversion to Judaism. As a result, according to Beth Shammai Halakhah, circumcision is the eighth law, which should be followed by complete Torah observance. These points are in sharp contrast to Beth Hillel Halakhah which does believe in salvation for non-Jews and makes circumcision the last step in conversion. There has always been a subcurrent of Rabbis who have maintained a tradition that Beth Shammai Halakhah will replace Beth Hillel Halakhah during the messianic era, although there is no documented source for the origin of this tradition.
