CANONICAL FORMS FOR 2-DIMENSIONAL LINEAR SYSTEMS OVER COMMUTAT IVE RINGS

Autor:	A. Sáez-Schwedt, Tomas Sanchez-Giralda
Rok vydání:	2002
Předmět:	Principal ideal ring Discrete mathematics Ring theory Ring (mathematics) Algebra and Number Theory Noncommutative ring Localization of a ring Polynomial ring Domain (ring theory) Ideal class group Mathematics
Zdroj:	Communications in Algebra. 30:2993-3011
ISSN:	1532-4125 0092-7872
DOI:	10.1081/agb-120004004
Popis:	In this paper we study the action of the feedback group on m-input, 2-dimensional linear dynamical systems over a commutative ring R, in order to calculate canonical forms. We define a set for each element g of R . For a class of systems, a complete set of canonical forms can be constructed associated with pairs , where f belongs to . If the ring is an elementary divisor domain, in particular a P.I.D., this method applies to all reachable systems. When R is a Dedekind domain, a formula is obtained for calculating using the factorization of gR in powers of prime ideals. We also establish two conditions on the ring which imply that each set , is finite. For the rings and , we calculate explicitely the canonical forms, improving by this way the known results about the number of feedback classes over these rings. Finally, effective calculations are made when R is the ring of integers of an algebraic field, using methods of Computational Algebra.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a7e9d267c84d0cdb3cd7faea9d3977cf https://doi.org/10.1081/agb-120004004 Zobrazit plný text záznamu