Lecture 6: Rings
نویسنده
چکیده
We have shown that Zn is a group under addition and Zn is a group under multiplication (set of all numbers co-prime to n in Zn). Till now, the two operations + and × have been treated differently. But from our experience with integers and even matrices, these operations satisfy properties like “distribution” (a(b+ c) = ab+ ac). Hence, after success in defining an abstract structure with one operation (group), now we define another abstract structure with 2 operations. The first question is, what should be the defining properties of this new abstract structure. We will be inspired by integers again and define the concept of Rings.
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