Or just "Alamein". Nobody in his or her right mind from Australasia would consider "Alamein" to refer to the place itself, today. I've heard old sojers say "I fought at Alamein."

But as for the others, algebra, alcohol and alchemy, the "al" portion is not brought to your attention by being separated from its noun, so unless you are an Arabic speaker you wouldn't even realise the implications. And English has such a terrible habit of grabbing something and running with it without any further analysis. I don't know what case "hoi" is, either (never studied Greek, me), but I did understand that it meant "the" or "those" or "this" or "that", depending on context, and that "polloi" meant "the people". But I still happily refer to "the hoi polloi"!

Ain't life grand?