A reduction theorem for the existence of \(\ast\)-clean finite group rings (Q1987115)
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scientific article; zbMATH DE number 7189019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A reduction theorem for the existence of \(\ast\)-clean finite group rings |
scientific article; zbMATH DE number 7189019 |
Statements
A reduction theorem for the existence of \(\ast\)-clean finite group rings (English)
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9 April 2020
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The paper under review deals with the existence of $*$-clean finite group rings in terms of solutions of some special congruence. The two main results (namely, Theorems 1.3 and 1.4), which are rather technical, are based on a series of other technical claims (namely, Lemmas 1.1 and 1.2) which technicalities reduce the proofs to the question of whether or not a specific congruence has a solution or not. The further considerations utilize a few more assertions from number theory, namely Lemmas 2.1 to 2.6.
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\(\ast\)-clean group ring
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2-adic valuation
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self-orthogonal abelian group code
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