Abstract
Tiled orders over discrete valuation ring have been studied since the 1970s by many mathematicians, in particular, by Yategaonkar V.A., Tarsy R.B., Roggenkamp K.W, Simson D., Drozd Y.A., Zavadsky A.G. and Kirichenko V.V. Yategaonkar V.A. proved that for every n > 2, there is, up to an isomorphism, a finite number of tiled orders over a discrete valuation ring O of finite global dimension which lie in $M_n(K)$ where K is a field of fractions of a commutatively discrete valuation ring O. The articles by R.B. Tarsy, V.A. Yategaonkar, H. Fujita, W. Rump and others are devoted to the study of the global dimension of tiled orders. H. Fujita described the reduced tiled orders in Mn(D) of finite global dimension for n = 4; 5. V.M. Zhuravlev and D.V. Zhuravlev described reduced tiled orders in Mn(D) of finite global dimension for n = 6: This paper examines the necessary condition for the finiteness of the global dimension of the tile order. Let A be a tiled order. The kernel of the projective resolvent of an irreducible lattice has the form M1f1 +M2f2 + ::: +Msfs, where Mi is irreducible lattice, fi is some vector. If the tile order has a finite global dimension, then there is a projective lattice that is the intersection of projective lattices. This condition is the one explored in the paper.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.