Zero-divisors of character rings of finite groups

Shoichi KONDO

doi:10.2969/jmsj/03040737

Shoichi KONDO

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 4 Pages 737-746

DOI https://doi.org/10.2969/jmsj/03040737

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Published: 1978 Received: April 26, 1977 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M.F. Atiyah, Characters and cohomology of finite groups, Inst. Hautes Études Sci. Publ. Math., 9 (1961), 23-64.
2) M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969.
3) B. Banaschewski, On the character rings of finite groups, Canad. J. Math., 15 (1963), 605-612.
4) N. Bourbaki, Commutative algebra, Hermann, Paris; Addison-Wesley, Reading, Mass., 1972.
5) C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
6) T. Gulliksen, P. Ribenboim and T. M. Viswanathan, An elementary note on group-rings, J. Reine Angew. Math., 242 (1970), 148-162.
7) S. Kondo, On the character rings of finite groups, Proc. Japan Acad., 49 (1973), 685-689.
8) S. Kondo, A remark on the character rings of finite groups, Proc. Japan Acad., 52 (1976), 98-101.
9) P. Roquette, Arithmetische Untersuchung des Charakterringes einer endlichen Gruppe, J. Reine Angew. Math., 190 (1952), 148-168.
10) J.-P. Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1971.
11) K. Shiratani, On the characters and the character rings of finite groups, Mem. Kyusyu Univ., 11 (1957), 99-115.
12) I. Sinha, 0-divisors in group rings, Proc. Amer. Math. Soc., 43 (1974), 476-477.
13) R. G. Swan, Induced representations and projective modules, Ann, of Math., 71 (1960), 552-578.
14) J.G. Thompson, A non-duality theorem for finite groups, J. Algebra, 14 (1970), 1-4.

Right : [1] M. F. Atiyah, Characters and cohomology of finite groups, Inst. Hautes Études Sci. Publ. Math., 9 (1961), 23-64.
[2] M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969.
[3] B. Banaschewski, On the character rings of finite groups, Canad. J. Math., 15 (1963), 605-612.
[4] N. Bourbaki, Commutative algebra, Hermann, Paris; Addison-Wesley, Reading, Mass., 1972.
[5] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
[6] T. Gulliksen, P. Ribenboim and T. M. Viswanathan, An elementary note on group-rings, J. Reine Angew. Math., 242 (1970), 148-162.
[7] S. Kondo, On the character rings of finite groups, Proc. Japan Acad., 49 (1973), 685-689.
[8] S. Kondo, A remark on the character rings of finite groups, Proc. Japan Acad., 52 (1976), 98-101.
[9] P. Roquette, Arithmetische Untersuchung des Charakterringes einer endlichen Gruppe, J. Reine Angew. Math., 190 (1952), 148-168.
[10] J. -P. Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1971.
[11] K. Shiratani, On the characters and the character rings of finite groups, Mem. Kyusyu Univ., 11 (1957), 99-115.
[12] I. Sinha, 0-divisors in group rings, Proc. Amer. Math. Soc., 43 (1974), 476-477.
[13] R. G. Swan, Induced representations and projective modules, Ann. of Math., 71 (1960), 552-578.
[14] J. G. Thompson, A non-duality theorem for finite groups, J. Algebra, 14 (1970), 1-4.

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