Solid varieties of semirings (Q2709037)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solid varieties of semirings |
scientific article |
Statements
7 November 2001
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varieties of semirings
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identities
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hyperidentities
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Solid varieties of semirings (English)
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A variety \(V\) is called solid, if every identity of \(V\) is also a hyperidentity of \(V\). In this paper the least and the greatest solid subvarieties for the variety of algebras \(S(+,\cdot)\) with the following identities are characterized: \(x+x=x\), \(xx=x\), \((x+y)+z=x+(y+z)\), \((xy)z=x(yz)\), \(x(y+z)=xy+xz\), \((x+y)z=xz+yz\), \(xy+z=(x+z)(y+z)\), \(x+yz=(x+y)(x+z)\), \(x+y+u+v=x+u+y+v\), \(xyuv=xuyv\).NEWLINENEWLINEFor the entire collection see [Zbl 0954.00028].
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