Kaley Cuoco filed for divorce on Friday, the same day she and Karl Cook announced their split after three years of marriage

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More details surrounding Kaley Cuoco's divorce from Karl Cook have surfaced.

According to Cuoco's divorce filing, obtained by PEOPLE, the Flight Attendant star, 35, has asked the court to terminate its ability to award spousal support to either herself or Cook, 30.

The documents — which were filed in Los Angeles Superior Court on Friday, the same day that Cuoco and Cook announced their split after three years of marriage — request that the former couple separate their property, with the actress keeping "miscellaneous jewelry and other personal effects" as well as her "earnings and accumulations ... before marriage, during marriage and from after the date of Separation."

"There are additional separate property assets and obligations of each party as mandated by the parties' Prenuptial Agreement," note the court papers, in which Cuoco also asks that she and Cook each be responsible for their own attorney's fees.

Cuoco cited irreconcilable differences as the reason for divorce; she did not specify the date of separation in her filing.

Kaley Cuoco and Karl Cook
Credit: Kevork Djansezian/NBCU Photo Bank/NBCUniversal via Getty Images

Cuoco, who is an avid equestrian, started dating Cook, also an equestrian, in 2016. They got engaged on her birthday in November 2017 and tied the knot on June 30, 2018.

The pair revealed their split in a joint statement to PEOPLE last week, saying, "Despite a deep love and respect for one another, we have realized that our current paths have taken us in opposite directions."

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"We have both shared so much of our journey publicly so while we would prefer to keep this aspect of our personal life private, we wanted to be forthcoming in our truth together. There is no anger or animosity, quite the contrary," the statement continued.

"We have made this decision together through an immense amount of respect and consideration for one another and request that you do the same in understanding that we will not be sharing any additional details or commenting further," they added.

Karl Cook, Kaley Cuoco
Kaley Cuoco and Karl Cook
| Credit: Jordan Strauss/Invision/AP/Shutterstock

Since announcing the split, Cuoco has been busy working on upcoming romantic-comedy Meet Cutein addition to starting production on season 2 of The Flight Attendant

A source tells PEOPLE in this week's issue that Cuoco "is doing fine," adding that the Big Bang Theory alum and Cook "haven't spent that much time together recently." 

"She has a lot going on in her career now and loves her work," the source says. "Their relationship is just following different paths. A marriage doesn't work if you rarely see the other one."