Ring Theory || Theorem" The Cancellation Laws Hold In A Ring R If And Only If R Has No Zero Divisor"
Автор: 𝐋𝐎𝐆𝐈𝐂 𝐋𝐀𝐍𝐄
Загружено: 2023-07-21
Просмотров: 3443
Описание:
In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the map from R to R that sends x to ax is not injective. Similarly, an element a of a ring is called a right zero divisor if there exists a nonzero y in R such that ya = 0
Definition. An integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Equivalently: An integral domain is a nonzero commutative ring with no nonzero zero divisors. An integral domain is a commutative ring in which the zero ideal {0} is a prime ideal.
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![If R is a Field then Polynomial Ring R[x] need not be a Field - Proof- ED - Lesson 24](https://image.4k-video.ru/id-video/9j5hhLOrkMI)
