(Bloomberg) -- Several candidates who back former President Donald Trump’s false claims of widespread election fraud won Republican primaries for governor, senator and attorney general Tuesday.

Governor, Pennsylvania

Nominee: Doug Mastriano

His record: As a state senator, he led the failed effort to overturn President Joe Biden’s win in the Keystone State, holding a public hearing that featured Trump on speaker phone; lobbying a top Justice Department official to investigate fraud claims; spending campaign money to bus supporters to Trump’s Jan. 6 “Stop the Steal” rally in Washington that preceded the US Capitol insurrection; and briefly overseeing a partisan audit of results.

What he’s said: “There is mounting evidence that the PA presidential election was compromised.” 

Why the race matters: As governor, Mastriano would appoint the secretary of state, the commonwealth’s top elections official. He’s pledged to decertify all of the state’s voting machines, appoint as secretary of state an unnamed “election integrity” expert who’s a “rock star” on the issue, and throw out all 8.7 million existing voter registrations and force everyone to re-register, a move that would be difficult under federal law.

General election opponent: Democratic Attorney General Josh Shapiro

US House, Pennsylvania

Nominee: Jim Bognet

His record: A former Trump administration official, Bognet called his own loss in a House race in 2020 suspicious and filed a lawsuit seeking to have the US Supreme Court throw out all late-arriving mail-in ballots, which tended to favor Democratic candidates. It was dismissed.

What he’s said: “On election night, I was up by over 10,000 votes, just like President Trump. But Governor Wolf changed the rules of the election in the middle of the election. We must audit the vote, and make sure that only legal ballots are counted in Pennsylvania. No more drop boxes. No more non-signature-verified mail-in ballots. And no more rigged elections.” 

Why the race matters: 139 US House members objected to the certification of the Electoral College vote in 2021. If he wins, Bognet would replace a Democrat who supported certification.

General election opponent: Incumbent Representative Matt Cartwright

US Senator, North Carolina

Nominee: Ted Budd

His record: As a member of the US House, Budd signed two public letters urging the Justice Department to investigate election fraud, signed an amicus brief supporting a Texas lawsuit asking the Supreme Court to intervene in the election, and voted against certifying electors from Arizona and Pennsylvania. When a clip of him saying Biden won the election circulated during the GOP primary, he said it was taken out of context. 

What he’s said: “Millions of Americans believe there were consequential problems in November’s presidential election. I’ve heard from an overwhelming number of my own constituents, and they share this belief. They witnessed voter safeguards unconstitutionally removed by non-legislative officials. They saw states with no signature verification, no voter ID laws, outdated voter rolls, poll watchers denied access to the count, and ballots accepted long after Election Day had passed.” 

Why the race matters: Eight senators objected to the certification of the Electoral College vote in 2021. If he wins, Budd would replace a Republican senator who supported certification.

General election opponent: Former state Supreme Court Chief Justice Cheri Beasley

US House, North Carolina

Nominee: Sandy Smith

Her record: She has repeatedly claimed that Trump won the 2020 election and attended his Jan. 6 rally in Washington.

What she’s said: “DONALD TRUMP WON” in a tweet.

Why the race matters: If she wins, Smith would replace a Democrat who supported certifying the Electoral College vote in 2021.

General election opponent: State Senator Don Davis

Attorney General, Idaho 

Nominee: Raúl Labrador 

His record: A former member of the US House, Labrador said that if he were attorney general at the time, he would have signed onto a Texas lawsuit seeking to get the Supreme Court to intervene in the 2020 election. Five-term incumbent Republican Attorney General Lawrence Wasden did not sign on, saying it would infringe on the state’s sovereignty. Labrador defeated Wasden in the primary.

What he’s said: “The basis of that lawsuit was that some states had not followed the Constitution broadly.”

Why the race matters: Attorneys general from 19 states joined the lawsuit, which sought to block electors from Georgia, Michigan, Pennsylvania, and Wisconsin from being counted. The Supreme Court declined to hear the case on the basis that the attorneys general lacked standing to bring the lawsuit.

General election opponent: Boise lawyer Steven Scanlin  

©2022 Bloomberg L.P.