these are polynomials as in given set {sum i=1-->n(ai.xi)| ai element of R}
i am asking how to show this is a field you are asking is this an integral domain,don't i have to show that this is an integral domain?and in my book there is a given theorem says:every field is an integral domain.i think i am confused when i translate in english.

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Wanderer, idolater, worshiper of fire,
Come even though you have broken your vows a thousand times,
Come, and come yet again.
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Jalāl ad-Dīn Muḥammad Rumi