Related papers: Decidability of the theory of modules over Pr\"ufe…
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Pr\"ufer (in particular B\'ezout) domains whose localizations at maximal ideals have dense value groups. For B\'ezout domains, these…
In this paper we give elementary conditions completely characterising when the theory of modules of a Pr\"ufer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is…
Let B be a commutative B\'ezout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable sets in terms, on one hand, of the definable sets in the…
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
We prove that the theory of all modules over the ring of algebraic integers is decidable.
Motivated by the Pontryagin-Hill criteria of freeness for abelian groups, we investigate conditions under which unions of ascending chains of projective modules are again projective. Several extensions of these criteria are proved for…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…
In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
In this note, we establish conditions under which the union of an increasing sequence of completely decomposable modules over domains are again completely decomposable. In our investigation, the condition of purity of modules is crucial. In…
We generalize known results on summands of completely decomposable and separable torsion-free abelian groups to modules over h-local Pr\"ufer domains. Over such domains summands of completely decomposable torsion-free modules are again…
We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.
If V is a finitely generated variety such that the first-order theory of the finite members of V is decidable, we show that V is residually finite, and in fact has a finite bound on the sizes of subdirectly irreducible algebras. This result…
We study questions around the existence of bounds and the dependence on parameters for linear-algebraic problems in polynomial rings over rings of an arithmetic flavor.In particular, we show that the module of syzygies of polynomials…
A classical problem, that goes back to the 1960's, is to characterize the integral domains R satisfying the property (IDn): "every singular nxn matrix over R is a product of idempotent matrices". Significant results, which describe this…
We show that every Dedekind domain $R$ lying between the polynomial rings $\mathbb Z[X]$ and $\mathbb Q[X]$ with the property that its residue fields of prime characteristic are finite fields is equal to a generalized ring of integer-valued…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…