Indeed, the tags to the question (both “commutative algebra” and “noncommutative algebra”), the notation (brackets are normally used for polynomial rings) and the previous comment by OP (about elements being invertible) send a mixed message here, so I wonder if there is a possible confusion. @Bumblebee, you should either make it abundantly clear whether you mean the free (noncommutative) algebra quotiented by a two-sided ideal, or the free commutative algebra (=polynomial ring) quotiented by an ideal!
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