John Gill Commentary 1 Kings 15

Now in the eighteenth year of King Jeroboam the son of Nebat
reigned Abijam over Judah .
] That is, began to reign; and by this it appears that Rehoboam was in the eighteenth year of his reign when he died, for he and Jeroboam began their reign at the same time.

Three years reigned he in Jerusalem
And three only; his reign was short, and indeed not three full years, only one whole year and part of two others; for Asa his son began to reign in the twentieth of Jeroboam, (1 Kings 15:9) so that he reigned part of his eighteenth, this whole nineteenth, and part of his twentieth:

and his mother's name was Maachah the daughter of Abishalom ;
called Absalom, (2 Chronicles 11:20 2 Chronicles 11:21) , generally supposed by the Jews to be Absalom the son of David, and which may seem not improbable, since his other two wives were of his father's family, (2 Chronicles 11:18) . Josephus says ^F17 she was the daughter of Tamar the daughter of Absalom, and so his granddaughter; and which may account for her being called Michaiah the daughter of Uriel of Gibeah, (2 Chronicles 13:2) since the difference between Maachah and Michaiah is not very great; and Uriel might be the name of Tamar's husband; though it is most likely that both father and daughter had two names; she seems to be mentioned here, to observe that she was the cause and means of her son's disagreeable walk, as follows, see (1 Kings 15:13) .

FOOTNOTES:

• F17: Antiqu. l. 8. c. 10. sect. 1.

And he walked in all the sins of his father, which he had done before him Having such bad examples as both parents to copy after; it chiefly respects idolatrous practices, see (1 Kings 14:23).

and his heart was not perfect with the Lord his God He did profess the true God, and worshipped him, but not wholly, and only, and sincerely; he worshipped other gods besides him: and so his heart was not

as the heart of David his father Who was a sole and sincere worshipper of God, never departed from him and his service.

Nevertheless, for David's sake did the Lord his God give him a
lamp in Jerusalem
A kingdom there, as the Targum, splendid and glorious, to be continued in his posterity: to set up his son after him; in it:

and to establish Jerusalem :
to continue that in which the temple was, for the sake of which, and the worship of God in it, there was a succession of David's posterity on the throne of Judah.

Because David did that which was right in the eyes of the Lord,
&c.] With respect to worship: and turned not aside from anything that he commanded him all the days of his life; especially in matters of religion, nor even in his moral walk and conversation, deliberately, studiously, and with design:

save only in the matter of Uriah the Hittite;
the killing of him, and other sins which led on to it, and were in connection with it; Abarbinel thinks, because the affair of Bathsheba is not mentioned, that was not reckoned to David as a sin; but no doubt it was, and is included here.