Projective resolution of irreducible modules over tiled order
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 323-336.

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

We indicate the method for computing the kernels of projective resolution of irreducible module over tiled order. On the base of this method we construct projective resolution of irreducible module and calculate the global dimension of tiled order. The evident view of kernels of projective resolution allows to check easily the regularity of tiled order.
Keywords: tiled order, projective resolution, distributive module
Mots-clés : kernel of epimorphism.
@article{ADM_2012_14_2_a13,
     author = {Viktor Zhuravlev and Dmytro Zhuravlyov},
     title = {Projective resolution of irreducible  modules over tiled order},
     journal = {Algebra and discrete mathematics},
     pages = {323--336},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a13/}
}
TY  - JOUR
AU  - Viktor Zhuravlev
AU  - Dmytro Zhuravlyov
TI  - Projective resolution of irreducible  modules over tiled order
JO  - Algebra and discrete mathematics
PY  - 2012
SP  - 323
EP  - 336
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a13/
LA  - en
ID  - ADM_2012_14_2_a13
ER  - 
%0 Journal Article
%A Viktor Zhuravlev
%A Dmytro Zhuravlyov
%T Projective resolution of irreducible  modules over tiled order
%J Algebra and discrete mathematics
%D 2012
%P 323-336
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a13/
%G en
%F ADM_2012_14_2_a13
Viktor Zhuravlev; Dmytro Zhuravlyov. Projective resolution of irreducible  modules over tiled order. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 323-336. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a13/

[1] Yu. A. Drozd, V. V. Kirichenko, Finite Dimensional Algebras, Springer-Verlag, Berlin–Heidelberg–New York, 1994 | MR

[2] J. of Soviet Math., 11:4, April (1979), 598–612 | DOI | MR

[3] Zh. T. Chernousova, M. A. Dokuchaev, M. A. Khibina, V. V. Kirichenko, S. G. Miroshnichenko, V. N. Zhuravlev, “Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets, I”, Algebra and Discrete Math., 1 (2002), 32–63 | MR

[4] Zh. T. Chernousova, M. A. Dokuchaev, M. A. Khibina, V. V. Kirichenko, S. G. Miroshnichenko, V. N. Zhuravlev, “Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets, II”, Algebra and Discrete Math., 2:2 (2003), 47–86 | MR

[5] M. Hazewinkel, N. Gubareni, V. V. Kirichenko, Algebras, Rings and Modules, v. 1, Mathematics and Its Applications, 575, Kluwer Acad. Publish., 2004, xii+380 pp. | MR

[6] M. Hazewinkel, N. Gubareni, V. V. Kirichenko, Algebras, Rings and Modules, v. 2, Mathematics and Its Applications, 586, Springer, Dordrecht, 2007, xii+400 pp. | DOI | MR

[7] V. V. Kirichenko, A. V. Zelensky, V. N. Zhuravlev, “Exponent matrices and tiled orders over discrete valuation rings”, Algebra and Computation, 15:5–6 (2005), 997–1012 | DOI | MR

[8] V. V. Kirichenko, M. A. Khibina, “Semi-perfect semi-distributive rings”, Infinite Groups and Related Algebraic Topics, Institute of Mathematics NAS Ukraine, 1993, 457–480 (in Russian) | MR

[9] A. A. Tuganbaev, Semidistributive modules and rings, Kluwer Acad. Publ., Dordrecht, 1998 | MR

[10] V. Zhuravlev, D. Zhuravlyov, “Tiled orders of width $3$”, Algebra and Discrete Math., 1 (2009), 111–123 | MR