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On the class group of D plus E[[Γ*]]
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DOI：10.1007/s10231-026-01657-5.png)
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Abstract
En 中文
In this paper, we study the class group structure of rings of the form D + E[[Gamma*]], where D subset of E is an extension of integral domains and G is a numerical semigroup. We examine the properties of t-invertible and v-invertible fractional ideals in these rings and investigate their relationship with the t-class group Clt(D) of the base domain D. Our primary results establish that the natural mapping phi : Clt(D) -> Clt(D + E[[Gamma*]]) is an injective homomorphism when E is a flat D-module, although it is not surjective in general. Furthermore, we provide a complete characterization of the t-invertible t-ideals of D+E[[Gamma*]] extended (with nonzero trace) to D. Specifically, we show that if E is completely integrally closed and qf(D) subset of E, then every t-invertible t-ideal I of D + E[[Gamma*]] with nonzero trace in D can be expressed as I= uJ(D + E[[Gamma*]]), for some u is an element of qf(D + E[[Gamma*]]), and a nonzero t-ideal J of D.
Keywords:
Class group
t-invertible
Numerical semigroup
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0.9
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