This time Dodgers’ Zack Greinke is NL pitcher of the month

And the rich get richer, or at least their trophy cabinet gets more crowded.

Zack Greinke has been named the National League pitcher of the month for August, an award that goes very well with the one Clayton Kershaw won in July. Best watch out for Ricky Nolasco in September.

It’s just possible that the Dodgers have baseball’s -- or at least the National League’s -- best one-two at the front of their rotation.

Greinke was brilliant, of course, in August. He went 5-0 with a 1.23 ERA in five starts. He struck out 30 and walked eight in 36 2/3 innings.

Which barely put him ahead of the Dodgers’ curve for the month, what with the staff posting a 2.07 ERA.

It’s the first time Greinke, 29, has earned the monthly award in the NL. In April 2009, he was the American League pitcher of the month while with the Royals. It was the same year he was the AL Cy Young winner.

Greinke, who signed a six-year, $147-million contract with the Dodgers in the off-season, is 14-3 with 2.78 ERA on the season.