Geodesic
The group $K_0$ of a~generalized matrix ring
Algebra i logika, Tome 52 (2013) no. 3, pp. 370-385.

Voir la notice de l'article provenant de la source Math-Net.Ru

We deal with a group $K_0$ of some category of modules over a generalized matrix ring (of order 2). The results obtained are applied to compute the group $K_0$ for the generalized matrix ring itself.
Keywords: group $K_0$, generalized matrix ring. 
@article{AL_2013_52_3_a5,
     author = {P. A. Krylov},
     title = {The group $K_0$ of a~generalized matrix ring},
     journal = {Algebra i logika},
     pages = {370--385},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_3_a5/}
}
TY  - JOUR
AU  - P. A. Krylov
TI  - The group $K_0$ of a~generalized matrix ring
JO  - Algebra i logika
PY  - 2013
SP  - 370
EP  - 385
VL  - 52
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2013_52_3_a5/
LA  - ru
ID  - AL_2013_52_3_a5
ER  - 
%0 Journal Article
%A P. A. Krylov
%T The group $K_0$ of a~generalized matrix ring
%J Algebra i logika
%D 2013
%P 370-385
%V 52
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2013_52_3_a5/
%G ru
%F AL_2013_52_3_a5
P. A. Krylov. The group $K_0$ of a~generalized matrix ring. Algebra i logika, Tome 52 (2013) no. 3, pp. 370-385. http://geodesic.mathdoc.fr/item/AL_2013_52_3_a5/

[1] P. A. Krylov, “Ob izomorfizme kolets obobschennykh matrits”, Algebra i logika, 47:4 (2008), 456–463 | MR | Zbl

[2] P. A. Krylov, “In'ektivnye moduli nad koltsami formalnykh matrits”, Sib. matem. zh., 51:1 (2010), 90–97 | MR | Zbl

[3] P. A. Krylov, A. A. Tuganbaev, “Moduli nad koltsami formalnykh matrits”, Fundament. i prikl. matem., 15:8 (2009), 145–211 | MR

[4] H. Chen, “Stable ranges for Morita contexts”, Southeast Asian Bull. Math., 25:2 (2001), 209–216 | DOI | MR | Zbl

[5] H. Chen, “Morita contexts with many units”, Commun. Algebra, 30:3 (2002), 1499–1512 | DOI | MR | Zbl

[6] A. Haghany, K. Varadarajan, “Study of modules over formal triangular matrix rings”, J. Pure Appl. Algebra, 147:1 (2000), 41–58 | DOI | MR | Zbl

[7] P. Loustaunau, J. Shapiro, “Morita contexts”, Non-commutative ring theory, Proc. Conf. (Athens/OH, USA, 1989), Lect. Notes Math., 1448, Springer-Verlag, Berlin, 1990, 80–92 | DOI | MR

[8] R. Khazal, S. Dascalescu, L. van Wyk, “Isomorphism of generalized triangular matrix-rings and recovery of tiles”, Int. J. Math. Math. Sci., 2003:9 (2003), 533–538 | DOI | MR | Zbl

[9] D. Sheiham, “Universal localization of triangular matrix rings”, Proc. Am. Math. Soc., 134:12 (2006), 3465–3474 | DOI | MR | Zbl

[10] Z. Xiao, F. Wei, “Commuting mappings of generalized matrix algebras”, Linear Algebra Appl., 433:11/12 (2010), 2178–2197 | DOI | MR | Zbl

[11] Y. Li, F. Wei, “Semi-centralizing maps of generalized matrix algebras”, Linear Algebra Apll., 436:5 (2012), 1122–1153 | DOI | MR | Zbl

[12] G. Tang, Y. Zhou, “Strong cleanness of generalized matrix rings over a local ring”, Linear Algebra Appl., 437:10 (2012), 2546–2559 | DOI | MR | Zbl

[13] R. K. Dennis, S. C. Geller, “$K_i$ of upper triangular matrix rings”, Proc. Am. Math. Soc., 56 (1976), 73–78 | MR | Zbl

[14] P. A. Krylov, A. V. Mikhalev, A. A. Tuganbaev, Endomorphism rings of Abelian groups, Algebras Appl., 2, Kluwer Acad. Publ., Boston, MA, 2003 | DOI | MR | Zbl

[15] D. M. Arnold, Finite rank torsion-free Abelian groups and rings, Lect. Notes Math., 931, Springer-Verlag, Berlin–Heidelberg–New York, 1982 | MR | Zbl

[16] X. Bass, Algebraicheskaya $K$-teoriya, Mir, M., 1973 | MR | Zbl

[17] Dzh. Milnor, Vvedenie v algebraicheskuyu $K$-teoriyu, Mir, M., 1974 | MR

[18] J. Rosenberg, Algebraic $K$-Theory and its applications, Grad. Texts Math., 47, Springer-Verlag, New York, NY, 1994 | DOI | MR

[19] V. Srinivas, Algebraic $K$-Theory, Prog. Math., 90, Birkhäuser, Boston, MA etc., 1991 | DOI | MR | Zbl

[20] K. Feis, Algebra: koltsa, moduli i kategorii, Mir, M., 1977