Irreducible element：Irreducible element
Irreducible element
Inalgebra,anirreducibleelementofanintegraldomainisanon-zeroelementthatisnotinvertibleandisnottheproductoftwonon-invertibleelements.。其他文章還包含有：「IntuitionbehindIrreducibleElementsandPrimeElements」、「Irreducibleelement(ringtheory)」、「IrreducibleElement」、「IrreducibleElement」、「irreducibleelementinnLab」、「Irreduciblepolynomial」、「Primeandirreducibleelements」
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Intuition behind Irreducible Elements and Prime Elements
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All factors of an irreducible element are trivial, being units or associates. In that sense it cannot be reduced to a simpler expression.
Irreducible element (ring theory)
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In a ring R which is an integral domain, we say that an element x ∈ R is irreducible if, whenever we write r = a × b , it is the case that (at least) one of a ...
Irreducible Element
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The irreducible element is the final element in the factorization process. That is, it is a factor that cannot be factored any further. If the domain of ...
Irreducible Element
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An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit).
irreducible element in nLab
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In a commutative ring, an element is irreducible if it is neither invertible nor the product of two non-invertible elements, with respect to the ...
Irreducible polynomial
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In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.
Prime and irreducible elements
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In this section the notion of prime integers are generalized into prime elements and irreducible elements in a commutative ring with 1. Definition 0.1. Let R be ...