The Latest on Tuesday at the Australian Open (all times local):

3:35 p.m.

Rod Laver finally got his Australian Open trophy, even if it took 47 years to do so.

When Laver won the title in 1969, the Australian Open didn't award replicas of the Norman Brookes trophy to the winner, as it does today.

After Serena Williams beat Maria Sharapova in the quarterfinals in the stadium named after the Australian great, Rod Laver Arena, the tournament finally awarded the man known as "Rocket" his replica trophy.

Stephen Healy, the president of Tennis Australia, said, "We're going to correct that omission today."

Laver went on to win the French Open, Wimbledon and U.S. Open in 1969, giving him his second Grand Slam. No male player has managed to replicate the feat since then.

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2:32 p.m.

Serena Williams has beaten Maria Sharapova for the 18th consecutive time, a 6-4, 6-1 win that advances the defending champion to the semifinals of the Australian Open.

Williams, seeking her seventh title here, broke fifth-seeded Sharapova's serve and clinched an entertaining first set on her fourth set points. She rolled to a 5-0 lead in the second set before Sharapova held serve.

Williams, who also beat 2008 champion Sharapova in the final here last year, also won the French Open and Wimbledon in 2015 and got within two wins of a calendar-year Grand Slam before losing in the U.S. Open finals.

The No. 1-ranked Williams twice received medical treatment, at the end of the first set and again after the third game of the second. It was not immediately apparent what was affecting her.

Williams, who improved her career record over Sharapova to 19-2, will play No. 4-seeded Agnieszka Radwanska in the semifinals.

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12:45 p.m.

Agnieszka Radwanska said she wouldn't be as nervous this time around after reaching a Grand Slam semifinal for the fifth time. She beat Carla Suarez Navarro 6-1, 6-3 in the quarterfinals.

Something daunting in her path to the title, though, is a semifinal against either six-time Australian Open champion Serena Williams or five-time major winner Maria Sharapova, who won the title at Melbourne Park in 2008 and has reached three other finals.

She says, "Right now I have nothing to lose. Hopefully (I'll) play my best tennis, otherwise I'll be in big trouble."

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12:35 p.m.

Fourth-seeded Agnieszka Radwanska has become the first player through to the Australian Open semifinals, overpowering Carla Suarez Navarro 6-1, 6-3 in the opening match at Rod Laver Arena on Tuesday.

It's the second time in three years that she's reached the final four at Melbourne Park, having advanced to the semifinals in 2014 when she lost to Dominika Cibulkova after beating defending champion Victoria Azarenka in the quarterfinals.

It was Radwanska's third win in four matches against Suarez Navarro.

Radwanska will play the winner of Tuesday's next match between No.1 Serena Williams and fifth-seeded Maria Sharapova.