Hilbert-Burch teoremasi

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. 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. Eisenbud (1995) yilda bayonot va isbot beradi.

Hisobot

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

$0\rightarrow R^{m}{\stackrel {f}{\rightarrow }}R^{n}\rightarrow R\rightarrow R/I\rightarrow 0$

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. $\operatorname {Fitt} _{1}I$ ning I, ya'ni f matritsasining m o'lchamli kichiklarining determinantlari tomonidan yaratilgan ideal hisoblanadi.

Manbalar

• Burch, Lindsay (1968), „On ideals of finite homological dimension in local rings“, Proc. Cambridge Philos. Soc., 64-jild, 941–948-bet, doi:10.1017/S0305004100043620, ISSN 0008-1981, MR 0229634, Zbl 0172.32302
• Eisenbud, David (1995), Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150-jild, Berlin, New York: Springer-Verlag, ISBN 3-540-94268-8, MR 1322960, Zbl 0819.13001
• Eisenbud, David (2005), The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry, Graduate Texts in Mathematics, 229-jild, New York, NY: Springer-Verlag, ISBN 0-387-22215-4, Zbl 1066.14001
• Hilbert, David (1890), „Ueber die Theorie der algebraischen Formen“, Mathematische Annalen (German), 36-jild, № 4, 473–534-bet, doi:10.1007/BF01208503, ISSN 0025-5831, JFM 22.0133.01, S2CID 179177713{{citation}}: CS1 maint: unrecognized language ()