Geodesic
Similarity invariants for matrices over a commutative Artinian chain ring
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 403-412 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose that $R$ is a commutative Artinian chain ring, $A$ is an $m\times m$ matrix over $R$, and $S$ is a discrete valuation ring such that $R$ is a homomorphic image of $S$. We consider $m$ ideals in the polynomial ring over $S$ that are similarity invariants for matrices over $R$, i.e., these ideals coincide for similar matrices. It is shown that the new invariants are stronger than the Fitting invariants, and that new invariants solve the similarity problem for $2\times 2$ matrices over $R$.
Keywords: commutative Artinian chain ring, discrete valuation ring, polynomial ring, ideal, similarity invariants, Fitting invariants. 
@article{MZM_2006_80_3_a9,
     author = {V. L. Kurakin},
     title = {Similarity invariants for matrices over a commutative {Artinian} chain ring},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--412},
     year = {2006},
     volume = {80},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a9/}
}
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V. L. Kurakin. Similarity invariants for matrices over a commutative Artinian chain ring. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 403-412. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a9/

[1] H. Fitting, “Die Determinantenideale eines Modulus”, Jahresber. Deutch. Math.-Verein., 46 (1936), 195–228 | Zbl | Zbl

[2] A. A. Nechaev, “O podobii matrits nad kommutativnym lokalnym artinovym koltsom”, Tr. seminara im. I. G. Petrovskogo, 9, 1983, 81–101 | MR | Zbl

[3] I. S. Cohen, “On the structure and ideal theory of complete local rings”, Trans. Amer. Math. Soc., 59:1 (1946), 54–106 | DOI | MR | Zbl

[4] A. A. Nechaev, “O stroenii konechnykh kommutativnykh kolets s edinitsei”, Matem. zametki, 10:6 (1971), 679–688 | MR | Zbl