On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms
On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms
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DOI：
10.1007/s10474-022-01270-x
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发表时间：
2022-02
影响因子：
0.9
通讯作者：
A. Geroldinger;F. Halter-Koch;Qinghai Zhong
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文献类型：
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作者：
A. Geroldinger;F. Halter-Koch;Qinghai Zhong
设G是一个可加有限交换群，是G的自同态群的子集. G上的序列是（-）加权零和序列，如果存在使得. 我们构造转移同态从范数幺半群（伽罗瓦代数数域与伽罗瓦群）和从幺半群的正整数，表示为二元二次型，到幺半群的加权零和序列。然后研究了加权零和序列幺半群的代数和算术性质。
LetGbe an additive finite abelian group andbe a subset of the endomorphism group ofG. A sequenceoverGis a (-)weighted zero-sum sequence if there aresuch that. We construct transfer homomorphisms from norm monoids (of Galois algebraic number fields with Galois group) and from monoids of positive integers, represented by binary quadratic forms, to monoids of weighted zero-sum sequences. Then we study algebraic and arithmetic properties of monoids of weighted zero-sum sequences.