We construct Artinian serial rings and tiled orders of width two with maximal finite global dimension.
Similar content being viewed by others
References
M. Hazewinkel, N. Gubareni, and V. V. Kirichenko, Algebras, Rings and Modules, Vol. 1, Kluwer, Dordrecht (2004).
W. H. Gustafson, “Global dimension in serial rings,” J. Algebra, No. 97, 14–16 (1985).
E. Kirkman and I. Kuzmanovich, “Global dimension of a class of tiled orders,” J. Algebra, No. 127, 57–92 (1989).
M. Hazewinkel, N. Gubareni, and V. V. Kirichenko, Algebras, Rings and Modules, Vol. 2, Springer, Dordrecht (2007).
L. A. Skornyakov, “On the case where all modules are serial,” Mat. Zametki, 5, No. 2, 173–182 (1969).
C. Faith, Algebra. II. Rings Theory, Springer, Berlin (1976).
G. Puninski, Serial Rings, Kluwer, Dordrecht (2001).
R. B. Warfield, Jr., “Serial rings and finitely presented modules,” J. Algebra, 37, 187–222 (1975).
M. A. Dokuchaev, V. V. Kirichenko, B. V. Novikov, and A. P. Petravchuk, “On incidence modulo ideal rings,” J. Algebra Appl., 6, No. 4, 553–586 (2007).
G. Michler, “Structure of semi-perfect hereditary Noetherian rings,” J. Algebra, 13, No. 3, 327–344 (1969).
D. Eisenbud and P. Griffith, “The structure of serial rings,” Pacif. J. Math., 36, 173–182 (1971).
A. W. Goldie, “Torsion-free modules and rings,” J. Algebra, 1, 268–287 (1964).
A. G. Zavadskii and V. V. Kirichenko, “Torsion-free modules above prime rings,” Zap. Nauch. Sem. LOMI, 57, 100–116 (1976).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 2, pp. 154–159, February, 2009.
Rights and permissions
About this article
Cite this article
Bronitskaya, N.A. Serial rings and tiled orders of width two. Ukr Math J 61, 188–194 (2009). https://doi.org/10.1007/s11253-009-0211-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0211-3