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喺數學,特別係代數入面,域係指一個非零交換環,當中唔係 嘅元素乘埋一齊都唔係 。域係整數環嘅推廣,係域上面我哋可以研究整除性。係域入面,每一個非零元素都有消除性質:如果 ,咁 。
域幾乎係所有地方都係咁樣定義,但係都有啲變體。有啲書唔要求域有乘法單元,又或者可以係唔交換環。係呢篇文入面,我哋要求域係要有乘法單元同埋係交換嘅。
域基本上被定義爲非零交換環,使得兩個非零嘅數乘埋都要係非零。用數學式寫出來,就係:
呢個定義可以用下面嘅方法去重寫:
一個好重要嘅性質係,場嘅每一個子環都係一個域,掉反轉,對每一個域,我哋都可以構作一個場(域中分數場),使得個域係個場嘅子環,呢個亦都可以作爲域嘅定義:
以下嘅環唔係域:
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