Possessive form: Others vs Others'

I’ve encountered these sentences in the net:

“My morals are mine, not others.” “Decisions are yours, not others.” “American values are ours, not others”.

I wonder whether they are correct regarding the possessive form of others. I think it should be others’ not others. For example, the first sentence should be

“My Morals are mine, not others’.”

I’ve searched the net with the words “possessive forms”, “possessive forms ending”, “possessive without noun”, “possessive omitting noun”, “possessive pronoun”, and other related words to find the correct possessive form that is without following noun (like others’, the book’s, the car’s. I don’t know what this form is called in English), but to no avail. I believe that, when I was a student (not a native English speaker one), I was taught that I could omit the noun after apostrophe s if it was understood what the omitted noun is. So the word others’ should be the correct word. But when I searched the net to check with these words - mine, not others’ / yours, not others’ / ours, not others’ – the word not others came up much more often than the word not others’.

That quite surprised and confused me. So, I posted a question here in hope that someone could help me.

The 2nd edited part:

And as I said, I’ve tried to learn more about the correct use of the possessive apostrophe s that is without a noun following but couldn’t. Now, I’m not sure what said was clear enough. To be more clear, the following is an example of what I’m trying to mean:

The golden key is this car’s key, not that car’s.

Is the use of < that car’s > in the above sentence correct, and is there a technical term for such a word (the use of apostrophe s without a noun following)? I’d like to learn more about it but don’t know what is(are) the word(s) to search.

Best regards,

Chirapat