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- Title
Small potential counterexamples to the pure semisimplicity conjecture.
- Authors
García, José L.
- Abstract
The pure semisimplicity conjecture or pssc states that every left pure semisimple ring has finite representation type. Let F , G be division rings, and assume we identify conditions on a F - G -bimodule B which are sufficient to make the triangular matrix ring G 0 B F into a left pure semisimple ring which is not of finite representation type. It is then said that those conditions yield a potential counterexample to the pssc. Simson [17–20] gave several such conditions in terms of the sequence of the left dimensions of the left dual bimodules of B. In this paper, conditions with the same purpose are given in terms of the continued fraction attached to B , and also through arithmetical properties of a division ring extension G ⊆ F.
- Subjects
MATHEMATICAL ability; RING extensions (Algebra); DIVISION rings; ISOMORPHISM (Crystallography); FRACTIONS
- Publication
Journal of Algebra & Its Applications, 2018, Vol 17, Issue 10, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498818501839