What is meant by a blessing without "Shem u'Malchut"?

Hello, wherever the poskim (halachic authorities) have written that one should recite a blessing without "Shem u'Malchut," it is permissible to say all the words of the blessing, but the words "Hashem Elokeinu" should be contemplated silently in the heart.

Sources: Regarding "Elokeinu," it is necessary to skip it, as explained in Shut HaRivash (Siman Taf) because there is a prohibition of taking Hashem's Name in vain by pronouncing "Elokeinu." See also what is written on this matter in Shut Yabia Omer, Part 10 (pages 131-136, paragraph 17).

However, it seems straightforward that it is permitted to say "Melech Ha'olam" (King of the Universe), as there is no prohibition here. This is explicitly stated in the aforementioned response of the Rivash. This is also the view of Pri Megadim, Orach Chaim (Siman Reish Tet, Mishbatzot Zahav, paragraph 133). See also Bi'ur Halacha (Siman Reish Yud, under "Ve'im") which cites Derech Pekudayich (Positive Commandment 30) that there is no prohibition against "Lo Tisa et Shem Hashem" (not taking Hashem’s Name in vain) by pronouncing "Melech Ha'olam." This is the simple approach taken in Shut Chelek Yaakov (Choshen Mishpat Orach Chaim Siman Nun Hei, under "Ve'iy") and Siman Nun Chet.

Also see Rema Even HaEzer (Siman Lamed Daled, Section Gimmel), Chelek Mechokek and Beit Shmuel (paragraph 106), Piskei Teshuva (paragraph 68), Shadei Chemed Part 1 (page 80), and Shut Shalmat Chaim (Siman 114).

With blessings, Hillel Meirs