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A Note on Euclidean Cyclic Cubic Fields


Affiliations
1 Institute of Mathematical Sciences, HBNI, CIT Campus, Taramani, Chennai - 600113, India
2 Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Chennai - 603103, India
     

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Let K be a cyclic cubic field and ΟK be its ring of integers. In this note we prove that all cyclic cubic number fields with conductors in the interval [73, 11971] and with class number one are Euclidean.
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  • D. Clark and M. Ram Murty, The Euclidean algorithm for Galois extensions, J. Reine Angew. Math., 459 (1995) 151–162. MR1319520 Zbl 0814.11049
  • H. J. Godwin and J. R. Smith, On the Euclidean nature of four cyclic cubic fields, Math. Comp., 60 (1993) 421–423. MR1149291 Zbl 0795.11055
  • M. Harper and M. RamMurty, Euclidean Rings of Algebraic Integers, Canad. J. Math., Vol. 56(1) (2004) 71–76. MR2031123 Zbl 1048.11080
  • H. Heilbronn, On Euclid’s algorithm in cubic self-conjugate fields, Proc. Cambridge Philosophical Soc., 46 (1950) 377–382. MR0035313 Zbl 0036.30101
  • J. W. Jones and D. P. Roberts, A database of number fields, LMS J. Comput. Math., 17(1) (2014) 595–618. MR3356048 Zbl 06638042.
  • F. Lemmermeyer, The Euclidean Algorithm in Algebraic Number Fields, Exposition. Math., 13 (1995) no. 5, 385–416. MR1362867 Zbl 0843.11046.
  • M. Ram Murty, K. Srinivas and M. Subramani, Admissible primes and Euclidean quadratic fields, to appear in JRMS.
  • J. R. Smith, On Euclid’s algorithm in some cyclic cubic fields, J. London Math. Soc., 44 (1969) 577–582. MR0240075 Zbl 0175.04501.

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  • A Note on Euclidean Cyclic Cubic Fields

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Authors

Srinivas Kotyada
Institute of Mathematical Sciences, HBNI, CIT Campus, Taramani, Chennai - 600113, India
Subramani Muthukrishnan
Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Chennai - 603103, India

Abstract


Let K be a cyclic cubic field and ΟK be its ring of integers. In this note we prove that all cyclic cubic number fields with conductors in the interval [73, 11971] and with class number one are Euclidean.

References