Prime radicals in up-monoid rings. (Q2890345)
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scientific article; zbMATH DE number 6044475
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prime radicals in up-monoid rings. |
scientific article; zbMATH DE number 6044475 |
Statements
8 June 2012
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unique product monoids
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unique product groups
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monoid rings
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lower nilradical
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upper nilradical
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prime rings
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semiprime rings
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reduced rings
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Prime radicals in up-monoid rings. (English)
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A monoid \(G\) is a `unique product monoid' (up-monoid) if for any two nonempty finite subsets \(A\) and \(B\) of \(G\), there is at least one \(c\in G\) which has a unique representation as \(c=ab\) with \(a\in A\) and \(b\in B\). Here the authors study the relationships between nil-related properties of a ring and those of the monoid ring \(RG\) where \(G\) is a up-monoid.NEWLINENEWLINE Direct proofs are given of the (known) results that a ring is semiprime (resp. prime, reduced, a domain) if and only if \(RG\) has the corresponding property. The lower nilradicals of monoid rings are also computed. Many examples of up-groups are given to which the results can be applied.
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