Is it permissible to greet people with the intention of a mere salutation, not as an act of worship or seeking reward, especially if the greeting only occurs upon meeting them?

Spreading greetings of peace (salam) is an act of worship that the Prophet, peace and blessings be upon him, encouraged due to the affection and love it fosters among Muslims. Its virtue increases by having the intention (niyyah) and seeking reward (ajr), as the Prophet, peace and blessings be upon him, said: "Indeed, actions are but by intentions." A person's greeting of peace to their brethren without having an explicit intention is permissible. However, what is prohibited is for it to be done out of showing off (riya') or for one to believe it is an act of worship and a means of drawing closer to people, because directing worship to other than Allah is polytheism (shirk).