irreducible
a . 不能復歸的,不能削減的不可約的
不能復歸的,不能削減的不可約的
irreducible 不可約
irreducible adj 1 :
incapable of being made smaller or simpler ; "
an irreducible minimum "; "
an irreducible formula "; "
an irreducible hernia " [
ant : {
reducible }]
Irreducible \
Ir `
re *
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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 implication "irreducible implies prime" is true in integral domains in which any two non-zero elements have a greatest common divisor This is for instance the case of unique factorization domains
What is an irreducible matrix? - Mathematics Stack Exchange What is an irreducible matrix? Ask Question Asked 6 years, 7 months ago Modified 6 years, 7 months ago
Prove that Spec $R$ is irreducible if and only if the radical ideal . . . 2 An easy way is to use the fact that irreducible components of the spectrum of a ring correspond to the minimal primes in the ring, see the Stacks Project
abstract algebra - Methods to see if a polynomial is irreducible . . . Given a polynomial over a field, what are the methods to see it is irreducible? Only two comes to my mind now First is Eisenstein criterion Another is that if a polynomial is irreducible mod p th
abstract algebra - difference between irreducible element and . . . Then, on the wikipedia page below, it says "an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials "
Irreducible polynomial means no roots? - Mathematics Stack Exchange The condition of being irreducible if it doesn't have any roots is false Consider, for example, the polynomial $$ x^4 + 4 x^2 + 3 = (x^2 + 1) (x^2 + 3) \in \mathbb {R} [x] $$ When the coefficient ring is not a field, though, some coefficients are not invertible The polynomial $$ 2x \in \mathbb {Z} [x]$$
Irreducibles are prime in a UFD - Mathematics Stack Exchange On the RHS, we know $a$ is irreducible If $d$ is invertible (i e an unit), then RHS only has $1$ irreducible element, which contradicts the definition of UFD
Show if these Gaussian integers are irreducible or not One is that if the norm of an element is a prime integer, then the element is irreducible in the Gaussian integers This shows that $1 \pm i$ and $2 \pm i$ are irreducible
Is an irreducible polynomial the minimal polynomial of its roots? 2 For completeness, the only (obvious) difference is that, by definition, a minimal polynomial is a monic irreducible polynomial, whereas an irreducible polynomial need not to be monic
linear algebra - Irreducible vs. indecomposable representation . . . However, Serre is dealing with finite-dimensional complex representations of finite groups, and in that case, yes, every indecomposable representation is irreducible