Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Computable categoricity for algebraic fields with splitting algorithms


Authors: Russell Miller and Alexandra Shlapentokh
Journal: Trans. Amer. Math. Soc. 367 (2015), 3955-3980
MSC (2010): Primary 03D45; Secondary 03C57, 12E05, 12L99
DOI: https://doi.org/10.1090/S0002-9947-2014-06093-5
Published electronically: October 20, 2014
MathSciNet review: 3324916
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A computably presented algebraic field $ F$ has a splitting algorithm if it is decidable which polynomials in $ F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of elements of $ F$ belong to the same orbit under automorphisms. We also show that this criterion is equivalent to the relative computable categoricity of $ F$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 03D45, 03C57, 12E05, 12L99

Retrieve articles in all journals with MSC (2010): 03D45, 03C57, 12E05, 12L99


Additional Information

Russell Miller
Affiliation: Department of Mathematics, Queens College – C.U.N.Y., 65-30 Kissena Boulevard, Flushing, New York 11367 – and – Ph.D. Programs in Mathematics and Computer Science, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016
Email: Russell.Miller@qc.cuny.edu

Alexandra Shlapentokh
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
Email: shlapentokha@ecu.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06093-5
Received by editor(s): November 3, 2011
Received by editor(s) in revised form: January 29, 2013
Published electronically: October 20, 2014
Additional Notes: The first author was partially supported by Grant # DMS–1001306 from the National Science Foundation, by Grant # 13397 from the Templeton Foundation, by the Centre de Recerca Matemática and the European Science Foundation, and by several grants from The City University of New York PSC-CUNY Research Award Program
The second author was partially supported by Grants # DMS–0650927 and DMS–1161456 from the National Science Foundation, by Grant # 13419 from the Templeton Foundation, and by an ECU Faculty Senate Summer 2011 Grant.
Article copyright: © Copyright 2014 American Mathematical Society