Abian's poset and the ordered monoid of annihilator classes in a reduced commutative ring. (Q2878805)
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scientific article; zbMATH DE number 6340461
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abian's poset and the ordered monoid of annihilator classes in a reduced commutative ring. |
scientific article; zbMATH DE number 6340461 |
Statements
5 September 2014
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Boolean monoids
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Abian order
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reduced rings
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partially ordered monoids
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Abian's poset and the ordered monoid of annihilator classes in a reduced commutative ring. (English)
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The authors deal with a reduced commutative ring \(R\) with \(1\neq 0\) and the set \(R_E\) of equivalence classes for the equivalence relation on \(R\) given by \(x\sim y\) if \(\mathrm{ann}_R(x)=\mathrm{ann}_R(y)\). They study \(R\) and \(R_E\) as monoids and as partially ordered sets. They are particularly interested in the question when \(R_E\) can be embedded in \(R\) either as a monoid or a partially ordered set.
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