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Gorenstein rings and inverse polynomials. (English) Zbl 0957.13005

Let \(R\) be a ring, \(S\) be a submonoid of \(\mathbb{N}\) and \(R[x^S]\) be the ring of all polynomials of the form \(\sum_{i\in S} r_ix^i\). It is shown that for so-called symmetric submonoids \(S\), \(R\) a Gorenstein ring implies \(R[x^S]\) a Gorenstein ring.

MSC:

13B25 Polynomials over commutative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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References:

[1] Enochs E., Canad. J.Math
[2] Enochs E., Houston. J. Math
[3] Iwanaga Y., Tsukuba J. Math 4 pp 107– (1980)
[4] DOI: 10.1093/qmath/25.1.359 · Zbl 0302.16027 · doi:10.1093/qmath/25.1.359
[5] DOI: 10.1080/00927879808826189 · Zbl 0931.13005 · doi:10.1080/00927879808826189
[6] DOI: 10.1112/jlms/s2-8.2.290 · Zbl 0284.13012 · doi:10.1112/jlms/s2-8.2.290
[7] DOI: 10.1080/00927879308824819 · Zbl 0794.16004 · doi:10.1080/00927879308824819
[8] DOI: 10.1007/BF01189824 · Zbl 0804.18009 · doi:10.1007/BF01189824
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