Algebra (AMS Chelsea Publishing)

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• Algebra starts as the art of manipulating sums, products, and powers of numbers. The rules for these manipulations hold for all numbers, so the manipulation may be carried out with letters standing for the numbers. It then appears that the same rules hold for various different sorts of numbers, rational, real, or complex, and that the rules for manipulation even apply to things such as transformations which are not numbers at all. An algebraic system, as we will study it, is thus a set of elements of any sort on which functions such as addition and multiplication operate, provided only that these operations satisfy certain basic rules. The rules for multiplication and inverse are axioms for a "group", those for addition, subtraction, and multiplication are axioms for a "ring", and the fun... (查看原文)

  赛义甫 3赞 2022-05-22 14:25:18

• A simple finite algebraic system arises from the familiar observation that one can add and multiply "even" and "odd" (integers) - according to the rules ... This amounts to giving binary operations of addition and multiplication on a set of just two elements 0 (even) and 1 (odd). (查看原文)

  Kerstin 2018-01-28 08:07:03