Is the word alguma the same in Brazilian and European Portuguese?

Yes

The word "alguma" is identical in meaning, spelling, and grammatical function in both Brazilian and European Portuguese. The only difference is in pronunciation. Brazilian Portuguese tends to be more "syllable-timed," meaning the vowels are more open and clearly articulated. In contrast, European Portuguese is more "stress-timed," which results in a significant reduction of unstressed vowels. In Portugal, the final "a" in "alguma" is often pronounced as a very short, neutralized, or "clipped" sound (close to a schwa), whereas in Brazil, it is more distinct and open.

Brazilian Portuguese Examples

1. Você tem alguma dúvida? (Do you have any doubt?)
2. Tem alguma coisa estranha acontecendo. (Something strange is happening.)
3. Você viu alguma pessoa passando por aqui? (Did you see any person passing by here?)
4. Existe alguma chance de eu ir? (Is there any chance of me going?)
5. Eu não encontrei alguma parte do mapa. (I didn't find some part of the map.)

European Portuguese Examples

1. Tens alguma dúvida? (Do you have any doubt?)
2. Há alguma coisa estranha a acontecer. (Something strange is happening.)
3. Viste alguma pessoa a passar por aqui? (Did you see any person passing by here?)
4. Existe alguma hipótese de eu ir? (Is there any chance of me going?)
5. Não encontrei alguma parte do mapa. (I didn't find some part of the map.)