Geodesic
Parabolic factorization for a matrix ring
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 219-227 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper, we prove Dennis–Vaserstein type decomposition (or a parabolic factorization) for some pairs of parabolic subsets $P_r$ and $\mathrm{MP}_s$ in the matrix ring $M(n,R)$ over Hermite ring $R$. We also formulate and prove analogous results for non-square matrices. 
@article{ZNSL_2013_413_a10,
     author = {K. B. Tsvetkov},
     title = {Parabolic factorization for a~matrix ring},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {219--227},
     year = {2013},
     volume = {413},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a10/}
}
TY  - JOUR
AU  - K. B. Tsvetkov
TI  - Parabolic factorization for a matrix ring
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 219
EP  - 227
VL  - 413
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a10/
LA  - ru
ID  - ZNSL_2013_413_a10
ER  - 
%0 Journal Article
%A K. B. Tsvetkov
%T Parabolic factorization for a matrix ring
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 219-227
%V 413
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a10/
%G ru
%F ZNSL_2013_413_a10
K. B. Tsvetkov. Parabolic factorization for a matrix ring. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 219-227. http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a10/

[1] K. Dennis, “Stability for $\mathrm K_2$”, Lect. Notes Math., 353 (1973), 85–94 | DOI | MR | Zbl

[2] L. N. Vasershtein, “Stabilizatsiya dlya klassicheskikh grupp nad koltsami”, Mat. Sb., 93(135):2 (1974), 268–295 | MR | Zbl

[3] A. A. Suslin, M. S. Tulenbaev, “Teorema o stabilizatsii dlya $\mathrm K_2$-funktora Milnora”, Zap. nauchn. semin. LOMI, 64, 1976, 131–152 | MR | Zbl

[4] N. A. Vavilov, S. S. Sinchuk, “Razlozheniya tipa Dennisa–Vasershteina”, Zap. nauchn. semin. POMI, 375, 2010, 48–60 | MR | Zbl

[5] N. A. Vavilov, S. S. Sinchuk, “Parabolicheskie faktorizatsii rasschepimykh klassicheskikh grupp”, Algebra i analiz, 23:4 (2011), 1–30 | MR

[6] B. V. Zabavsky, “Diagonalizability theorems for matrices over rings with finite stable range”, Algebra Discrete Math., 1 (2005), 151–165 | MR | Zbl

[7] I. Kaplansky, “Elementary divisors and modules”, Trans. Amer. Math. Soc., 66:2 (1949), 464–491 | DOI | MR | Zbl