| 引用本文: | 周泽滋.关于最大公因数与最小公倍数概念的推广及其应用举例.[J].国防科技大学学报,1983,(3):133-138.[点击复制] |
| Zhou Zezi.A Generalized Concept of Greatest Common Factor and Least Common Multiple With Applied Examples[J].Journal of National University of Defense Technology,1983,(3):133-138[点击复制] |
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| 关于最大公因数与最小公倍数概念的推广及其应用举例 |
| 周泽滋 |
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| 摘要: |
| 本文运用通常最大公因数与最小公倍数的性质以引入非空整数组的最大公因数与最小公倍数的概念，并运用它引入群元素的特征数和环与域的特征数，此外论证了任意非空整数组必存在最大公因数和最小公倍数，且对于确定的非空整数组它们是唯一的。 |
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| 投稿日期：1983-04-26 |
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| A Generalized Concept of Greatest Common Factor and Least Common Multiple With Applied Examples |
| Zhou Zezi |
| Abstract: |
| In this paper，we have given a concept of greatest common factor and least common multiple in the nonempty set of integers with the nature of usual greatest common factor and least common multiple. Applying this concept，we incorpoate the characteristic number of a group's element and the characteristic numbers of a ring and field. Besides，We have proved that the greatest common factor and the least common muliple are existential for every nonempty set of integers and，unique for definite nonempty set of integers. |
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