Modules over semihereditary Bezout rings

Shores, Thomas S.

doi:10.1090/S0002-9939-1974-0349663-4

Modules over semihereditary Bezout rings
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by Thomas S. Shores

Proc. Amer. Math. Soc. 46 (1974), 211-213

DOI: https://doi.org/10.1090/S0002-9939-1974-0349663-4

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Abstract:

It is shown that every commutative semihereditary Bezout ring of Krull dimension at most one is an elementary divisor ring. A consequence is that the ring of polynomials in one indeterminate over a von Neumann regular ring is an elementary divisor ring.

References

Eléments de mathématique

Algèbre commutative

Modules plats

36

Stephen U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457–473. MR 120260, DOI 10.1090/S0002-9947-1960-0120260-3
Leonard Gillman and Melvin Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956), 362–365. MR 78979, DOI 10.1090/S0002-9947-1956-0078979-8

Semigroup rings as Prüferrings

Melvin Henriksen, Some remarks on elementary divisor rings. II, Michigan Math. J. 3 (1955/56), 159–163. MR 92772
Irving Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949), 464–491. MR 31470, DOI 10.1090/S0002-9947-1949-0031470-3
Irving Kaplansky, Infinite abelian groups, Revised edition, University of Michigan Press, Ann Arbor, Mich., 1969. MR 0233887
Max D. Larsen, William J. Lewis, and Thomas S. Shores, Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1974), 231–248. MR 335499, DOI 10.1090/S0002-9947-1974-0335499-1
P. J. McCarthy, The ring of polynomial over a von Neumann regular ring, Proc. Amer. Math. Soc. 39 (1973), 253–254. MR 316496, DOI 10.1090/S0002-9939-1973-0316496-3