Hilbert-Burch teoremasi sahifasining manbasini koʻrish

[[Matematika|Matematikada]] '''Hilbert-Burch teoremasi''' proyektiv o'lchamga ega bo'lgan taqdirda mahalliy yoki darajali halqaning bir qismining ba'zi erkin ruxsatlarining tuzilishini juda yaxshi tavsiflaydi.&nbsp;2.Hilbert                 (polinomli halqalar uchun bu teoremaning yangi versiyasini isbotladi va Burch (umumiyroq versiyani ham isbotladi. Keyinchalik bir qancha boshqa mualliflar bu teoremaning o'zgarishlarini qayta kashf qildilar va nashr etdilar. {{Harvard citation text|Eisenbud|1995}} yilda bayonot va isbot beradi.

== Hisobot ==
Agar ''R'' ideal ''I'' va bilan mahalliy halqa bo'lsa quyidagicha

: <math> 0 \rightarrow R^m\stackrel{f}{\rightarrow} R^n \rightarrow R \rightarrow R/I\rightarrow 0</math>

''R'' - modulning erkin o'lchamlari ''R''/''I'', keyin ''m''=''n''-1 va ideal ''I'' ''aJ'', bunda ''a'' ''R'' va ''J'' ning muntazam elementi, chuqurlik-2 ideal, birinchi Fitting ideal deyiladi. <math>\operatorname{Fitt}_1 I</math> ning ''I'', ya'ni ''f'' matritsasining ''m'' o'lchamli kichiklarining [[Aniqlovchi (matematika)|determinantlari]] tomonidan yaratilgan ideal hisoblanadi.

== Manbalar ==

* {{Citation |last=Burch |first=Lindsay |title=On ideals of finite homological dimension in local rings |work=Proc. Cambridge Philos. Soc. |volume=64 |pages=941–948 |year=1968 |doi=10.1017/S0305004100043620 |issn=0008-1981 |mr=0229634 |zbl=0172.32302}}
* {{Citation |last=Eisenbud |first=David |title=Commutative algebra. With a view toward algebraic geometry |volume=150 |year=1995 |series=[[Graduate Texts in Mathematics]] |place=Berlin, New York |publisher=[[Springer-Verlag]] |isbn=3-540-94268-8 |mr=1322960 |zbl=0819.13001 |author-link=David Eisenbud}}
* {{Citation |last=Eisenbud |first=David |title=The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry |volume=229 |year=2005 |series=[[Graduate Texts in Mathematics]] |place=New York, NY |publisher=[[Springer-Verlag]] |isbn=0-387-22215-4 |zbl=1066.14001 |author-link=David Eisenbud}}
* {{Citation |last=Hilbert |first=David |title=Ueber die Theorie der algebraischen Formen |work=[[Mathematische Annalen]] |volume=36 |issue=4 |pages=473–534 |year=1890 |language=German |doi=10.1007/BF01208503 |issn=0025-5831 |jfm=22.0133.01 |s2cid=179177713 |author-link=David Hilbert}}
[[Turkum:Matematik funktsiya andozasi]]
[[Turkum:Matematik asboblar]]
[[Turkum:Matematik belgilashlar]]