On euclidean rings
DOI:
https://doi.org/10.22199/S07160917.1997.0001.00003Abstract
In this article we extend the concept of Euclidean rings and Motzkin's work to commutative rings (not necessarily with an identity).
References
[ 1 ] Agargun, A.G., and Fletcher, C.R., " Euclidean rings", Doa Tr. J. Math .. 19. pp. 291- 399, (1995).
[ 2 ] Amano, K., , “A note on Euclidean ring", Bull. Fac:. Gen. Ed. Gifu Univ .. No.20. pp. 13- 15, (1985).
[ 3 ] Fletcher, C.R .. "Euclidean rings". J. London Math. Soc:., (2), 4, 79-82, (1971 ) .
[ 4 ] Hiblot. .J . .J .. “Des anneaux euclidiens dont le plus petit algorithme n'est pas valeurs finies". Comptes Rendues, 281, srie A-411-414, (1975).
[ 5 ] Hiblot. J.J .. " Correction une note sur les anneaux euclidiens", Comptes Rendues.284. srie A-847, (1977).
[ 6 ] Kanemitsu. M. and Yoshida, K., ''Euclidean rings", Bull. Fac. Sci., Ibaraki Univ. Math .. No.18. (1986).
[ 7] Lenstra. H.W.. Lectures on Euclidean Rings, Bielefeld, Summer (1974).
[ 8] Motzkin, T., "The Euclidean algorithm", Bull. Amer. Math. Soc., 55, pp. 1142- 1146, (1949).
[ 9 ] Nagata. M.. ''On Euclidean algorithm". Tata Inst. Fund. Res. Studies in Math.. 8. pp. 175- 186. (1978) .
[10] Nagata. M.."Some remarks on Euclid rings", J. Math. Kyoto Univ., pp. 25- 3. pp. 421 - 422. (1985).
[11] Nagata, M., "On the definition of a Euclidean ring", Advanced Studies in Pure Mathematic:s. 11, pp. 167- 171, (1987).
[12] Samuel. P ..”About Euclidean rings'', Journal of Algebra, 19, pp. 282-301. ( 1971).
[ 2 ] Amano, K., , “A note on Euclidean ring", Bull. Fac:. Gen. Ed. Gifu Univ .. No.20. pp. 13- 15, (1985).
[ 3 ] Fletcher, C.R .. "Euclidean rings". J. London Math. Soc:., (2), 4, 79-82, (1971 ) .
[ 4 ] Hiblot. .J . .J .. “Des anneaux euclidiens dont le plus petit algorithme n'est pas valeurs finies". Comptes Rendues, 281, srie A-411-414, (1975).
[ 5 ] Hiblot. J.J .. " Correction une note sur les anneaux euclidiens", Comptes Rendues.284. srie A-847, (1977).
[ 6 ] Kanemitsu. M. and Yoshida, K., ''Euclidean rings", Bull. Fac. Sci., Ibaraki Univ. Math .. No.18. (1986).
[ 7] Lenstra. H.W.. Lectures on Euclidean Rings, Bielefeld, Summer (1974).
[ 8] Motzkin, T., "The Euclidean algorithm", Bull. Amer. Math. Soc., 55, pp. 1142- 1146, (1949).
[ 9 ] Nagata. M.. ''On Euclidean algorithm". Tata Inst. Fund. Res. Studies in Math.. 8. pp. 175- 186. (1978) .
[10] Nagata. M.."Some remarks on Euclid rings", J. Math. Kyoto Univ., pp. 25- 3. pp. 421 - 422. (1985).
[11] Nagata, M., "On the definition of a Euclidean ring", Advanced Studies in Pure Mathematic:s. 11, pp. 167- 171, (1987).
[12] Samuel. P ..”About Euclidean rings'', Journal of Algebra, 19, pp. 282-301. ( 1971).
Published
2018-04-04
How to Cite
[1]
A. Goksel Agargun, “On euclidean rings”, Proyecciones (Antofagasta, On line), vol. 16, no. 1, pp. 23-36, Apr. 2018.
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