Invalidate the Prayer - Ruling on saying salaam to one who is praying

Is it mustahhab to say"assalam alaikum" aloudwhen one enters the
hallin the masjid where people are praying ? Andif it is should a
person who enters the hall say"assalam alaikum" aloudeven if the
Jamaah for the salaah has begun and it might disturb the khushoo of
the jamaah ?I am asking this questionsince few of our brothers say
"assalam alaikum" aloud even when the imam is reciting in the loud
prayers.
Praise be to Allaah.
The majority of scholars are of the view that it is permissible to say
salaam to the one who ispraying if that will not lead to spoiling of
the prayer of one who is unaware of the things that invalidate the
prayer, because he may think that it is obligatoryto return the
salaams verbally, so he will reply and thus invalidate his prayer. The
Hanafis are of the view that it is makrooh.
It says in Tabyeen al-Haqaa'iq: It is makrooh to say salaam to one who
is praying, reading Qur'aan, sitting to pass judgement, researching a
fiqhi matter or is relieving hismelf, and if one does say salaams to
them, it is not obligatory for them to respond, because it is
inappropriate. End quote.
In Sharh al-Kharashi 'ala Mukhtasar Khaleel (a Maaliki book) (1/325)
it says: It is not makrooh tosay salaams to one who is praying either
an obligatory or a naafil prayer. End quote.
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo' (a
Shaafa'ibook) (4/105): The words of our companions suggest thatit is
not makrooh to say salaam to one who is praying. This is what is
suggested by the saheehahaadeeth. End quote.
Shaykh Muhammad ibn 'Uthaymeen said in Liqa' al-Baab il-Maftooh
(24/31): Saying salaams to one who is praying is permissible because
the Prophet (peace and blessings of Allaah be upon him) did not
criticize those who greeted him with salaam. But if the Muslimfears
that he may confuse the worshipper, then he should not say salaams, or
if he fears that he may talk and reply – i.e., because mostof the
common folk do not understand so if you say salaam to them they may
reply Wa 'alayka al-salaam, thus invalidating their prayer– if he
knows that the prayer will be invalidated thereby. Whatever the case,
we say that saying salaams to one who is praying is not wrong, because
the Prophet (peace and blessings of Allaah be upon him) approved of
it, unless there is the fear that the person whois greeted may be
confused or his prayer may be invalidated, in which case one should
not say salaams.
But how should he respond? He should not respond verbally by saying
'Alayka al-salaam,rather he should respond by means of a gesture, by
raising his hand so that the one who greeted him will know that he has
returned the greeting. Then if the one who greeted him is still there
when he has said the salaam and finished his prayer, he may respond
verbally, but if the person has left, then the one who was greeted
does not have to do anything more than what was mentioned, namely
gesturing. The apparent meaning of the text is that returningthe
greeting is obligatory but he is excused from speaking because it
invalidates the prayer. End quote.
There is nothing wrong with saying salaam to one who is praying, but
if it is going to disturb the worshippers, such assaying salaam when
the imam is reciting, then one should not say salaam.
And Allaah knows best.