# Model-theoretic Algebra with Particular Emphasis on Fields, Rings, Modules

@inproceedings{Wilmers2006ModeltheoreticAW, title={Model-theoretic Algebra with Particular Emphasis on Fields, Rings, Modules}, author={George M. Wilmers}, year={2006} }

been omitted from an introductory text; the Lachlan-Kotlarski-Krajewski results on satisfaction classes are certainly difficult, but they have hitherto played a marginal role in the mainstream development of the field. On the other hand, I feel that the author missed an opportunity by not including any account of the development in the last ten years of connections between weak arithmetic and computational complexity, a development to which he himself has made a significant contribution. These…

No Paper Link Available

## 27 Citations

### On two tame algebras with super-decomposable pure-injective modules

- Mathematics
- 2011

Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland G3 of length 3 and the incidence k-algebra…

### On Wild Algebras and Super-Decomposable Pure-Injective Modules

- MathematicsAlgebras and Representation Theory
- 2022

Assume that k is an algebraically closed field and A is a finite-dimensional wild k-algebra. Recently, L. Gregory and M. Prest proved that in this case the width of the lattice of all pointed…

### On the Wild Rank Conjecture of Han

- Mathematics
- 2008

The concept of rank of a wild algebra, introduced by Y. Han in (8), is discussed and, after a slight modiflcation, investigated by means of Tarski's quantifler elimination theorem. This method…

### On the Wild Rank Conjecture of

- Mathematics
- 2009

The concept of rank of a wild algebra, introduced by Y. Han in [8], is discussed and, after a slight modification, investigated by means of Tarski’s quantifier elimination theorem. This method…

### ALGEBRAIC COMPACTNESS OF ∏ Mα / ⊕ Mα

- Mathematics
- 2004

In this note, we are working within the category RMod of (unitary, left) R-modules, where R is a countable ring. It is well known (see e.g. Kie lpiński & Simson [5], Theorem 2.2) that the latter…

### Exactness of direct limits for abelian categories with an injective cogenerator

- MathematicsJournal of Pure and Applied Algebra
- 2019

### A Note on Periodicity in Representation Theory of Finite Dimensional Algebras

- Mathematics
- 2006

Let Λ be an algebra over an algebraically closed field K of infinite transcendence degree over its prime subfield. We prove in particular that if every s-dimensional indecomposable nonprojective…

## References

SHOWING 1-3 OF 3 REFERENCES

### Model theory and modules

- Mathematics
- 1988

Abstract The model-theoretic investigation of modules has led to ideas, techniques and results which are of algebraic interest, irrespective of their model-theoretic significance. It is these aspects…

### Elementary duality of modules

- Mathematics
- 1993

Let R be a ring. A formula φ(x) in the language of left R-modules is called a positive primitive formula (ppf) if it is of the form ∃y(AB) (x/y) = 0 where A and B are matrices of appropriate size…

### This book is the third and last volume of a treatise on projective spaces over a

- This book is the third and last volume of a treatise on projective spaces over a