Following the prayers of supplication after the Amidah, Half-Kaddish is recited. On days on which Tachanun is not said, the Half-Kaddish is recited immediately after the Amidah. The reason that only Half-Kaddish is recited is to prevent interruption between the Amidah and Kaddish-Titkabal, which is recited after Kedushah d’Sidra. As long as the chazan has not recited Kaddish-Titkabal, he has not yet completely finished the Amidah repetition. Therefore, the chazan need not take three steps back upon the conclusion of the Amidah repetition, for he separates from prayer by taking three steps back at the end of Kaddish-Titkabal. On Mondays and Thursdays, when the Torah is read, Half-Kaddish is also recited after the Torah reading. We already learned that after Kedushah d’Sidra, the chazan recites Kaddish-Titkabal.
After Shir Shel Yom, Full-Kaddish is recited, the Kaddish said after the recital of Scriptural verses. Customarily, mourners are the ones to recite this Kaddish, for its recital possesses benefit for the elevation of the deceased person’s soul (see earlier in this book 4:5-6). If no mourner is present, one who does not have a parent recites it. However, if there is no one there who has lost a parent, it is customary not to recite this Kaddish, for, since it is normally recited by mourners, it is unbecoming for one whose parents are both alive to recite it.
After Pitum HaKetoret, Kaddish d’Rabbanan is recited, for it was instituted to be recited after rabbinic study. This type of Kaddish is also usually recited by mourners. When there is no one present who has lost a parent, it is customary not to recite it. In principle, the correct practice is that the chazan recites it, because it is not called Mourner’s Kaddish. However, since orphans have become accustomed to reciting it, many treat it like Mourner’s Kaddish.
The Chachamim greatly praise the virtue of this Kaddish, and teach that after the destruction of the Temple, it is one of the things in whose merit the world stands (Sotah 49a). The reason for this is because it is recited after a group of people (at least ten) learn Torah, and hence, its recital combines the mitzvah of Torah study, equivalent to all the mitzvot, and the sanctification of Hashem’s Name (Rashi).