I understand that Dunya means this world, and that Akhira mean the hereafter. Now, can Akhira refer to heaven or hell? Or does it mean the life after death?
What are the Islamic words for Hell and Heaven, especially as referenced in the Quran.
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There is a site which you can use to learn about the conceptual relations between the words in Quran: Ontology of Quranic Concepts.
If you go to the entry for afterlife locations it list two main places: Paradise (الجنة), Hell (جهنم) and if you go to their entries you can find other related words:
PS: Ontology of Quranic Concepts doesn't seem to be complete and there are some words which are not in the graph in general but it is a good source to check.
general names are below
heaven,Paradise:Janna(جَنَّة)(pl. جَنّات jannat) link:[2:82]
heaven:جَنَّاتُ عَدْنٍ(reference[16:31]), دَارُ السَّلَامِ(reference[6:127])etc.
hell:النَّارِ(means fire)(reference[2:39]), الْجَحِيمِ(reference[5:10]), سَقَرَ(reference[54:48]or[74:42])etc.