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Multiplication Rings Via Their Total Quotient Rings

Published online by Cambridge University Press:  20 November 2018

Malcolm Griffin
Malcolm Griffin*
Affiliation:
Queen's University, Kingston, Ontario
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In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letter N exclusively for nilpotents of the ring A.

A ring such that, given any two ideals L and M with L ⊆ M there exists an ideal Q such that L = QM is called a multiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called a Dedekind ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 430 - 449
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Gilmer, R. W., On a classical theorem of Noether in ideal theory, Pacific J. Math. 13 (1963), 579–583.Google Scholar
2. Gilmer, R. W. and Mott, J. L., Multiplication rings as rings in which ideals with prime radical are primary, Trans. Amer. Math. Soc. 114 (1965), 40–52.Google Scholar
3. Griffin, M. P., Valuations and Prufer rings, Can. J. Math. 26 (1974), 412–429.Google Scholar
4. Kaplansky, I., Projective modules, Ann. of Math. 68 (1958), 372–377.Google Scholar
5. Larsen, M. D. and McCarthy, P. J., Multiplicative theory of ideals (Academic Press, New- York, 1971).Google Scholar
6. Marot, J., Anneaux héréditaires commutatifs, C. R. Acad. Sc. Paris Sér. A 269 (1969), 58–61.Google Scholar
7. Mori, S., Uber allgemeine Multiplikationsringe. I, J. Sci. Hiroshima Univ. Ser. A-I Math. 4 (1934), 1–26.Google Scholar
8. Pierce, R. S., Modules over commutative regular rings , Mem. Amer. Math. Soc. (Providence, 1967).Google Scholar
9. Storrer, H. H., Epimorphisen von kommutativen Ringen, Comment. Math. Helv. 48 (1968), 378–381.Google Scholar