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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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##### References:
 [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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