An iterative construction of bases for finitely generated modules over principal ideal domains

Finitely-generated modules over a principal ideal domain

Let R be a commutative ring throughout. Usually R will be an integral domain and even a principal ideal domain, but these assumptions will be made explicitly. Since R is commutative, there is no distinction between left, right and 2-sided ideals. In particular, for every ideal I we have a quotient ring R/I. F always denotes a field. Our goal is to prove the classification theorem for finitely-g...

Higher algebraic K-theory of finitely generated torsion modules over principal ideal domains

The main purpose of this paper is computing higher algebraic K-theory of Koszul complexes over principal ideal domains. The second purpose of this paper is giving examples of comparison techniques on algebraic K-theory for Waldhausen categories without the factorization axiom.

Whitehead Modules over Large Principal Ideal Domains

We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.’s of size ≥ א2 have nonfree Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if ExtR(M,R) = 0. The second author proved that the problem of whether every Whitehead Z-module is free is independent of ZFC + GCH (cf. [5], ...

(C, A)-Invariance of Modules over Principal Ideal Domains

For discrete-time linear systems over a principal ideal domain three types of (C;A)-invariance can be distinguished. Connections between these notions are investigated. For pure submodules necessary and su cient conditions for dynamic (C;A)-injection invariance are given. Su cient conditions are obtained in the general case. Mathematical Subject Classi cations (1991): 93B07, 93B99, 15A33, 13C99

SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains