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On generalized integral representations over Dedekind rings. (English. Russian original) Zbl 0999.16500

J. Math. Sci., New York 89, No. 2, 1154-1158 (1998); translation from Zap. Nauchn. Semin. POMI 227, 113-118 (1995).
Summary: Let \(A\) be a Dedekind domain, \(k\) its quotient field and \(\Lambda\) a finitely generated algebra over \(A\). Then a generalized integral representation of \(\Lambda\) over \(k\) is a homomorphism from \(\Lambda\) into the ring of endomorphisms of some finitely generated module over \(k\) and an integral representation is a representation by matrices over \(k\). The author proves that any integral representation is equivalent to some generalized integral representation of \(\Lambda\).

MSC:

16G30 Representations of orders, lattices, algebras over commutative rings
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References:

[1] D. K. Faddeev, ”Introduction to the multiplicative theory of modules of integral representations”,Trudy MIAN,80, 145–182 (1965).
[2] E. Steiniz, ”Rechteckige system und moduln in Algebraishen Zahlkörpern I, II,”Math. Ann.,71, 328–354;72, 297–345 (1912). · JFM 42.0230.02 · doi:10.1007/BF01456849
[3] C. Chevalley,L’arithmétique dans les Algèbres de Matrices, Actual. Scient. et Industr. No. 323, Paris (1936).
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