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Wild representation type and undecidability. (English) Zbl 0735.16011
In this note it is proved that the theory of \(A\)-modules over a finite- dimensional wild algebra \(A\) is undecidable provided the following condition holds: Given any finite-dimensional algebra \(C\) there exists a finite-dimensional module \(B_ A\) whose endomorphism ring is of the form \(C\oplus I\) with an ideal \(I\), \(B\) is free as a \(C\)-module and there is a \(C\)-basis containing an element with annihilator equal to \(I\). Furthermore, some remarks concerning the validity of this condition are added.
Reviewer: W.Zimmermann

MSC:
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16B70 Applications of logic in associative algebras
16P10 Finite rings and finite-dimensional associative algebras
16G30 Representations of orders, lattices, algebras over commutative rings
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[1] DOI: 10.1112/plms/s3-56.3.451 · Zbl 0661.16026
[2] Prest, M. 1985. ”Tame categories of modules and deciability”. University of Liverpool. preprint
[3] Prest, M. 1988. London Math. soc. Lecture Note Series. Conference. 1988, Cambridge and New York, London. Cambridge University Press
[4] Prest M., J.Lodon Math. soc. 38 pp 403– (1988)
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