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Decidability of epimorphisms of dimension groups and certain modules

Published online by Cambridge University Press:  19 September 2008

K. H. Kim
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36195, USA
F. W. Roush
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, Alabama 36195, USA
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Abstract

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We give an algorithm for deciding the existence of epimorphisms of finitely additively generated Z[t] modules and dimension groups. This shows that the existence of eventual right resolving shift factor maps for mixing finite type shifts is decidable.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[1]Boyle, M., Marcus, B. & Trow, P.. Resolving maps and the dimension group for shifts of finite type. Memoirs of the Amer. Math. Soc. (Amer. Math. Soc, Providence, RI, 1987).CrossRefGoogle Scholar
[2]Borevich, Z.I. & Shafarevich, I. R.. Zahlentheorie. Birkhauser: Basel, 1966.Google Scholar
[3]Cartan, H. & Eilenberg, S.. Homological Algebra. Princeton University Press: Princeton, 1956.Google Scholar
[4]Grunewald, F.. Solution of conjugacy problems in certain arithmetic groups. In Adian, S. I., Boone, W. W., Higman, G., eds., Word Problems II, pp. 101139. North-Holland: Amsterdam, 1980.CrossRefGoogle Scholar
[5]Grunewald, F. & Segal, D.. Some general algorithms. I. Arithmetic groups, Ann. Math. 112 (1980), 531583.Google Scholar
[6]Grunewald, F. & Segal, D.. Decision problems concerning S-arithmetic groups. J. Symp. Logic 50 (1985), 734772.Google Scholar
[7]Kim, K.H. & Roush, F. W.. Some results on decidability of shift equivalence. J. Comb., Inf. & Sys. Sci. 4 (1979), 123146.Google Scholar
[8]Kim, K. H. & Roush, F. W.. Decidability of shift equivalence. Dynamical Systems, ed., Alexander, J. C.. Lecture Notes in Mathematics 1342 (Springer Verlag, Berlin, 1988).Google Scholar
[9]Kim, K. H. & Roush, F. W.. Undecidability of module homomorphisms. Proc. Amer. Math. Soc., 104 (1988), 374376.CrossRefGoogle Scholar
[10]Serre, J., Modules projectifs et espaces fibrés ?à fibre vectorielle. Algebra et Théorie des Nombres. Seminaire Dubreil: Paris, 1958.Google Scholar