Albert Barnes Commentary 1 Kings 11:5

"For Solomon went after Ashtoreth the goddess of the Sidonians, and after Milcom the abomination of the Ammonites." — 1 Kings 11:5 (ASV)

Went after - This expression is common in the Pentateuch and always signifies actual idolatry (Deuteronomy 13:2; Deuteronomy 28:14, etc.).

For Ashtoreth, or Astarte, the goddess of the Zidonians, see the notes on Exodus 34:13 and Deuteronomy 16:21. On the tomb of a Phoenician king, discovered in 1855 on the site of Sidon, mention is made of a temple of Astarte there, which the monarch built or restored, and his mother is said to have been a priestess of the goddess.

Milcom or Molech (1 Kings 11:7) are variants of the term ordinarily used for “king” among the Semitic races of Western Asia, which appears in names such as Melkart (Phoenician), Abimelech (Hebrew), Adrammelech (Assyrian), Abd-ul-malik (Arabic), etc. On the character and worship of Molech, see the note on Leviticus 20:2-5.