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irreducible    
a. 不能复归的,不能削减的不可约的

不能复归的,不能削减的不可约的

irreducible
不可约

irreducible
adj 1: incapable of being made smaller or simpler; "an
irreducible minimum"; "an irreducible formula"; "an
irreducible hernia" [ant: {reducible}]

Irreducible \Ir`re*du"ci*ble\, a.
1. Incapable of being reduced, or brought into a different
state; incapable of restoration to its proper or normal
condition; as, an irreducible hernia.
[1913 Webster]

2. (Math.) Incapable of being reduced to a simpler form of
expression; as, an irreducible formula.
[1913 Webster]

{Irreducible case} (Alg.), a particular case in the solution
of a cubic equation, in which the formula commonly
employed contains an imaginary quantity, and therefore
fails in its application. -- {Ir`re*du"ci*ble*ness}, n. --
-- {Ir`re*du"ci*bly}, adv.
[1913 Webster]

90 Moby Thesaurus words for "irreducible":
a certain, an, any, any one, atomic, austere, bare, basic,
called for, chaste, deep-seated, either, elementary, esoteric,
essential, exclusive, fundamental, homely, homespun, homogeneous,
immanent, implanted, implicit, inalienable, indicated,
indispensable, individual, indivisible, indwelling, inextricable,
infixed, ingrained, inherent, inner, integral, internal, intrinsic,
inward, inwrought, irreductible, irreplaceable, lone, mere,
monadic, monistic, monolithic, necessary, needed, needful,
of a piece, one, plain, prerequisite, primal, primary, private,
pure, pure and simple, required, requisite, resident, secret,
severe, simon-pure, simple, single, singular, sole, solid,
solitary, spare, stark, subjective, unadorned, unalienable,
unanalyzable, unchallengeable, uncluttered, undifferenced,
undifferentiated, undivided, unforgoable, uniform, unique, unitary,
unquestionable, unsolvable, vital, wanted, whole


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  • How do the definitions of irreducible and prime elements differ?
    The most widespread terminology would be “irreducible” for that case However there's no international math police, so everybody is entitled the right of naming concepts as they like; surely, using “prime” for “irreducible” doesn't do a good service to students $\endgroup$ –
  • Relation between irreducibility and reducedness for schemes
    An irreducible scheme that is reduced: irreducible + reduced is equivalent to integral, see here You can think of many examples by yourself You can think of many examples by yourself Irreducible scheme that is not reduced: $\mathrm{Spec}(k[t] (t^2))$
  • abstract algebra - What is meant by a polynomial that is irreducible . . .
    $\begingroup$ I would also comment that what I said about polynomial division was for polynomials over a field $\mathbb{F}$ $\mathbb{Z}$ is not a field, but due to Gauss's lemma being irreducible over $\mathbb{Q}$ is the same as being irreducible over $\mathbb{Z}$, so irreducible is the same as being prime $\endgroup$ –
  • abstract algebra - Methods to see if a polynomial is irreducible . . .
    This can be proved via an application of model theory: note that the statement "a given polynomial over $\mathbb{Z}$ is irreducible in some field" can be phrased via first-order logic So if it is true in algebraically closed fields of arbitrarily high characteristic, it is true over $\mathbb{C}$, even $\endgroup$
  • How do I find out if a polynomial is irreducible?
    Being a quartic, this polynomial is reducible if and only if it has a linear or quadratic factor with integer coefficients
  • About irreducible morphisms - Mathematics Stack Exchange
    Proving irreducible representation splits into direct sum of two irreducible representations when restricted to normal subgroup 2 Why are morphisms between non-isomorphic indecomposable modules always radical?
  • What is an irreducible matrix? - Mathematics Stack Exchange
    Therefore, it cannot be broken into smaller strongly connected components and that's why it is called irreducible E g $\pmatrix{0 1\\ 1 0}$ is irreducible while $\pmatrix{1 1\\ 0 1}$ is reducible (node 2 is reachable from node 1, but node 1 is not reachable from node 2)
  • Proving that a polynomial is irreducible over a field
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • abstract algebra - $1 +\sqrt {-n}$ is irreducible in $\mathbb {Z . . .
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • abstract algebra - difference between irreducible element and . . .
    This shows you can factor this polynomial into a product of two non-units, so it is $\textbf{not}$ irreducible This definition just means, $3$ is still irreducible even though you can factor it $(-3)\cdot (-1)$ Since $-1$ is a unit, it doesn't count as a factorization which would make it fail to be irreducible





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