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Periodic modules over general quantum Laurent polynomials. (English. Russian original) Zbl 0924.16006

Math. Notes 61, No. 1, 9-15 (1997); translation from Mat. Zametki 61, No. 1, 10-17 (1997).
We preserve the notation of the preceding review Zbl 0924.16005. The author continues with investigation of finitely generated \(A\)-modules [initiated in Mat. Zametki 59, No. 4, 497-503 (1996; Zbl 0879.16013), Mat. Sb. 185, No. 7, 3-12 (1994; Zbl 0849.16003)]. The main result is: if \(M\) is a non-zero finitely generated periodic (i.e. torsion) \(A\)-module then \(M\) is cyclic and there exists a basis \(Y_1,\dots,Y_n\) of \(G\) such that \(M\) is finitely generated projective over the subalgebra generated by \(D\) and \(Y_1,\dots,Y_{n-1}\).

MSC:

16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16S36 Ordinary and skew polynomial rings and semigroup rings
16S35 Twisted and skew group rings, crossed products
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
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References:

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