54,058 research outputs found
Representation embeddings and the second Brauer-Thrall conjecture
We prove that over an algebraically closed field there is a representation
embedding from the category of classical Kronecker-modules without the simple
injective into the category of finite-dimensional modules over any
representation-infinite finite-dimensional algebra. We also sharpen some known
results on representation embeddings, we simplify some proofs and we construct
a simultaneous orthogonal embedding for an infinite family of module
categories. In the last section the minimal classes of representation-infinite
algebras are determined. The result depends on the characteristic
On a Partial Decision Method for Dynamic Proofs
This paper concerns a goal directed proof procedure for the propositional
fragment of the adaptive logic ACLuN1. At the propositional level, it forms an
algorithm for final derivability. If extended to the predicative level, it
provides a criterion for final derivability. This is essential in view of the
absence of a positive test. The procedure may be generalized to all flat
adaptive logics.Comment: 18 pages. Originally published in proc. PCL 2002, a FLoC workshop;
eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai
(http://floc02.diku.dk/PCL/
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