пива (as partitive gen.) here sounds really weird to me, like you're pouring it out of a can into something else, and putting that in the fridge. If it's a can you can emphasise it with a number e.g. я поставил одну банку пива в холодильник :)

not a native speaker, just living and studying russian in moscow

It was noted below that this is properly called the partitive case; the Wikipedia articles have good examples in the vein of "А не испить ли нам чаю":[1][2]

[1]https://en.wikipedia.org/wiki/Partitive_case#Russian

[2]https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D1%82%D0%B8...

The partitive here is to express that the speaker is not specifying in what form or shape the beer in the fridge should appear. For a native speaker it sounds like you are talking about some quantity of beer but omitted the quantity so it's literally just some unspecified quantity of beer.

So you would say that though? Like I've just never heard my хозяйка квартиры say that is all. I hear it often in things like "would you like some tea/beer?" etc or "i'm going to buy some tea/beer" but never like that. My impression was that outside of those contexts it's not popular. Mind sharing some examples? Would be really useful! :)

You probably would never hear somebody saying "Поставь пива в холодильник." since, while a correct sentence, it would need some rare circumstances to be said. Поставь here is much more concrete than "put", it's more like "place" and I could imagine saying this only if I had been managing the fridge at some party and noticed it's running out of beer so I requested somebody to add more beer there. Much more common would be "Принеси/достань/возьми пива из холодильника" (get some beer from the fridge).

>You probably would never hear somebody saying "Поставь пива в холодильник." since, while a correct sentence, it would need some rare circumstances to be said. [...] I could imagine saying this only if I had been managing the fridge at some party and noticed it's running out of beer

Yup, pretty much that. Or like that one time when we went binge-shopping on craft beers, but there was only enough space in the fridge for a couple of bottles; so that was a normal request about an hour before we were to watch a movie. Which is pretty much the exact situation you described :)

I think "пива" is the partitive case, though.

That's exactly it! [1]

I'm a native speaker, and I wasn't even aware of partitive case. They never taught us about it, even though a mind-numbing amount of time was spent cramming the name of the usual six cases into our heads.

I only got more interested in linguistics after moving to the US, and, sadly, only took one class in college on it.

Thanks for noticing this, I just learned something!

As a side note, I also mixed up genitive and accusative cases.

[1]https://en.wikipedia.org/wiki/Partitive_case#Russian

I think the definitive and most authoritative review of the Russian grammatical cases was done by Zaliznyak: http://inslav.ru/images/stories/pdf/2002_Zalizniak_RIS_i_sta..., in Russian, pages 36-55. Fascinating reading.