High Quality Content by WIKIPEDIA articles! In mathematics, the total quotient ring, or total ring of fractions, is a construction that generalizes the notion of the field of fractions of a domain to rings that may have zero divisors. The idea is to formally invert as many elements of the ring as possible without trivializing the ring. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".

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