
Review of Short Phrases and Links 
This Review contains major "Nonzero Element" related terms, short phrases and links grouped together in the form of Encyclopedia article.
 An ideal of integers which contains a nonzero element contains a least positive element.
 In other words, a field is a commutative ring with identity in which every nonzero element has an inverse.
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 Generalized permutation matrix A square matrix with precisely one nonzero element in each row and column.
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 The sedenions are an algebra in which every nonzero element has a multiplicative inverse, but which has nonetheless divisors of zero, i.e.
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 A ring or an algebra in which every nonzero element has a multiplicative inverse is called a division ring resp.
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Nonzero Element
 Division ring or skew field A ring in which every nonzero element is a unit and 1≠0 is a division ring.
 In abstract algebra, a nonzero element a of a ring is a left zero divisor if there exists a nonzero b such that ab = 0.
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 A field is a commutative ring (F,+,*) in which 0≠1 and every nonzero element has a multiplicative inverse.
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Categories
 Zero Divisor
 Skew Field
 Multiplicative Inverse
 Nonzero
 Square Matrix

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