is 0 irreducible
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「is 0 irreducible」文章包含有：「Irreducibleelement」、「irreducibleelementsincommutativeringswith」、「Irreduciblepolynomial」、「irreduciblepolynomialinnLab」、「IrreduciblePolynomials」、「Isthezeroofafieldirreducible?」、「Sinceallirreducibleelementsarenonunits...」、「Whatisthedefinitionofanirreduciblepolynomial?Whydo...」、「Why0isnotirreducible?」
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Irreducible element
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In algebra, an irreducible element of an integral domain is a non-zero element that is not invertible and is not the product of two non-invertible elements.
irreducible elements in commutative rings with
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equivalent: (1) 0 is irreducible, (2) 0 is strongly irreducible, (3) 0 is very strongly irreducible, (4) 0 is prime, and (5) R is an integral domain.
Irreducible polynomial
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In some sense, almost all polynomials with coefficients zero or one are irreducible over the integers. More precisely, if a version of the Riemann ...
irreducible polynomial in nLab
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Notice that under this definition, the zero polynomial is not considered to be irreducible. An alternative definition, which applies to the ...
Irreducible Polynomials
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Is the zero of a field irreducible?
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Take the first. 0 should not be considered irreducible. – Daniel Fischer.
Since all irreducible elements are non units ...
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There is no point in allowing units to be irreducible as that is uninteresting. In a ufd non-zero prime elements are the same as irreducibles.
What is the definition of an irreducible polynomial? Why do ...
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A polynomial p(x) over a field F, of degree 2 or 3 is irreducible, if and only if it does not have any zero(root) in F. All the monic ...
Why 0 is not irreducible?
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It turns out that using such definitions yields that 0 is irreducible iff the ring is a domain (for all notions of associate and irreducible).