About determiners: The book became famous right after (its, the?) publication.

[Palych]

Are any determiners necessary in these sentences?

The book became famous right after (its, the?) publication.

The measures where necessary, otherwise (the?) inflation could gain a dangerous momentum. (the current process of inflation is meant)

Thank you.

[Mister Micawber]

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Unnecessary, but your second is not a sentence.

The book became famous right after publication.

The measures must be implemented where necessary; otherwise, inflation could gain a dangerous momentum.
.
_________________
Native English teacher at Mister Micawber's

[Palych]

Oops, I apologize. It had to be

"The measures were necessary, otherwise (the?) inflation could gain a dangerous momentum. (the current process of inflation is meant)".

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And three questions more:

"The button should be pushed with the (a?) thumb".
"The (?) people who has love for music are more happy".
"The (?) dogs having long tails look more licable".

Thank you.

[Cisco795]

"The measures were necessary, otherwise inflation could gain a dangerous momentum. (the current process of inflation is meant)". No "the".

"The button should be pushed with the thumb". Not "a""
"People who has love for music are more happy". No "the"
"Dogs With long tails look more likeable/likable". Not "the"

As a general English grammar rule the usage of the direct article (the) states that a writer/speaker should use it when his readers/listeners would know what he is referring about, and/or the noun that it is used with, has been previously mentioned. (Neither dog nor people had been previously mentioned by the writer/speaker).

A person that is about to push a button should know exactly what finger to use, even though the word (noun) thumb had not been previously mentioned in the sentence.

As of the dogs and the people, the reader/listener wouldn`t know either for sure. In this sentence I include "the dogs" and "the people" in the mix on purpose to emphasize my comment, now you (the reader) know what I am talking about).

God bless you.
Cisco.
_________________
Please, always correct me if I have made any kind of mistakes in my posts.

[Palych]

Thank you for your comments but, of course, I know these foggy rules. Let's look at how they work:

"... A person that is about to push a button should know exactly what finger to use" - most people have two hands and therefore two thumbs. What thumb should the person use?

Do English-speakers mean that saying "John is one of the most famous writers" the speaker implies that someplace in the world there is the (a?) list of the most famous writers? Anyway, the listener should do some work to find out who the famous writers are.
The "exactness" of "The people who have love for music are more happy" looks similar - the speaker implies a (the?) definite group of people but the listener has the capacity to create a list of such people. The same comment can be referred to "dogs with long tails".

And one comment-question more. You wrote: "... the usage of the direct article (the) states that a writer/speaker should use it when his readers/listeners would know what he is referring about, and/or the noun that it is used with, has been previously mentioned."
I think it should be corrected as: "... the noun that it is used with calls an (the?) object which has been previously mentioned.

You changed "having" with "with" - do you mean that to say "this dog has a long tail" is incorrect?

And, I assume, you meant "the definite article", not "the direct article".

Thank you.

[Cisco795]

"... A person that is about to push a button should know exactly what finger to use" - most people have two hands and therefore two thumbs. What thumb should the person use?"

Either one, but is going to use one finger out of the two, which means that any person reading that sign will know how to proceed.

"Do English-speakers mean that saying "John is one of the most famous writers" the speaker implies that someplace in the world there is the (a?) list of the most famous writers are":

In this sentence "the" is part of "most", it has nothing to do with "John".
A superlative (most) must be preceded by "the" (NOTE: Not always, but in your sentence it is required the use of it). By reading your sentence I, the reader, understand that he (the writer/speaker) is addressing a group of people that either knows John or they are all interested in the same topic, therefore there is a common knowledge as of whom John might be or will definitely find out about him with ease.

"The (?) people who has love for music are more happy".
"People who has love for music "are happier". (Oops, we both missed on that one).

"And one comment-question more. You wrote: "... the usage of the direct article (the) states that a writer/speaker should use it when his readers/listeners would know what he is referring about, and/or the noun that it is used with, has been previously mentioned."
I think it should be corrected as: "... the noun that it is used with calls an (the?) object which has been previously mentioned"

I appreciated the correction, my wording wasn`t the best, but I am glad the idea got across

"You changed "having" with "with" - do you mean that to say "this dog has a long tail" is incorrect?"
No, I sure don`t. (simple present) Correct.
"... having longtails.." (present continuos) Wrong.
That`s why I used the preposition "with".

"And, I assume, you meant "the definite article", not "the direct article".
These names vary from book to book, although they are both correct.

I truly enjoyed your reply, helps me checking up on myself and I love it, I take it as a agreeable challenge. Thank you so much.

God bless you and merry Christmas.
Cisco.
_________________
Please, always correct me if I have made any kind of mistakes in my posts.

[Palych]