參考文獻 |
[1] H. Bass, K-theory and stable algebra, Inst. Hautes Etudes Sci. Publ. Math. 22 (1964), 5-60.
[2] H. Bass, Algebraic K-Theory, Benjamin, New York, 1968.
[3] W.-Y. Chang, On a paper of P. M. Cohn, Master thesis, National Central University, Chung-li, Taiwan, 2015.
[4] W.-Y. Chang, C.-R. Cheng, and M.-G. Leu, A remark on the ring of algebraic integers in Q(√?-d), Israel Journal of Mathematics 216 (2016), 605-616.
[5] C.-A. Chen, About k-stage Euclidean rings, Ph.D. thesis, National Central University, Chung-li, Taiwan, 2011.
[6] C.-A. Chen and M.-G. Leu, The 2-stage Euclidean algorithm and the restricted Nagata′s pairwise algorithm, J. Algebra 348 (2011), 1-13.
[7] P. M. Cohn, On the structure of the GL2 of a ring, Inst. Hautes Etudes Sci. Publ. Math. 30 (1966), 5-53.
[8] G. E. Cooke, A weakening of the Euclidean property for integral domains and applications to algebraic number theory I, J. Reine Angew. Math. 282 (1976), 133-156.
[9] K. Dennis, B. Magurn, and L. Vaserstein, Generalized Euclidean group rings, J. Reine Angew. Math. 351 (1984), 113-128.
[10] G. Dresden, Resultants of cyclotomic polynomials, Rocky Mountain J. Math. 42:5 (2012), 1461-1469.
[11] D. S. Dummit and R. M. Foote, Abstract Algebra, 3rd ed., John Wiley and Sons, New York, 2003.
[12] A. J. Hahn and O. T. O′Meara, The Classical Groups and K-Theory, Springer-Verlag, New York, 1989.
[13] T. W. Hungerford, Algebra, Springer-Verlag, New York, 1974.
[14] T. Y. Lam, Bass′s work in ring theory and projective modules, in: T. Y. Lam, A. R. Magid (Eds.), Algebra, K-theory, Groups,
and Education, on the Occasion of Hyman Bass′s 65th Birthday, Contemp. Math. 243 (1999), 83-124.
[15] T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 2001.
[16] A. Leutbecher, Euklidischer Algorithmus und die Gruppe GL2, Math. Ann. 231 (1978), 269-285.
[17] B. A. Magurn, An Algebraic Introduction to K-Theory, Cambridge University Press, Cambridge, 2002.
[18] B. A. Magurn, On a note from Oliver concerning generalized Euclidean group rings, Comm. Algebra 42 (2014), 3350-3365.
[19] J. M. Masley and H. L. Montgomery, Cyclotomic elds with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256.
[20] H. Matsumura, Commutative Ring Theory, translated from the Japanese by M. Reid, 2nd ed., Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge, 1989.
[21] C. P. Milies and S. K. Sehgal, An Introduction to Group Rings, Kluwer Academic Publishers, Dordrecht, 2002.
[22] J. Neukirch, Algebraic Number Theory, Springer-Verlag, Berlin Heidelberg, 1999.
[23] D. S. Passman The Algebraic Structure of Group Rings, John Wiley and Sons, New York, 1977.
[24] S. Perlis and G. L. Walker, Abelian group algebras of nite order,
Trans. Amer. Math. Soc. 68 (1950), 420-426.
[25] P. Ribenboim, Rings and Modules, John Wiley and Sons, New York, 1969.
[26] P. Samuel, About Euclidean rings, Journal of Algebra 19 (1971), 282-301.
[27] A. A. Suslin, On the structure of the special linear group over polynomial rings, Mathematics of the USSR-Izvestiya, 11:2 (1977), 221-238.
[28] A. R. Tambunan, On generalized Euclidean rings, Master thesis, National Central University, Chung-li, Taiwan, 2017.
[29] L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funktsional. Anal. i Prilozhen. 5:2 (1971), 17-27.
[30] L. C. Washington, Introduction to Cyclotomic Fields, 2nd ed., Springer-Verlag, New York, 1997. |