Absolutely pure semimodules. (Q2911222)
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scientific article; zbMATH DE number 6081643
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Absolutely pure semimodules. |
scientific article; zbMATH DE number 6081643 |
Statements
12 September 2012
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absolutely pure semimodules
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finitely injective semimodules
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f-injective semimodules
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Fieldhouse regular semimodules
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Absolutely pure semimodules. (English)
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A semimodule \(M\) over a semiring \(R\) is called absolutely pure if it is pure in every semimodule containing it as a subsemimodule. The authors extend some properties of absolutely pure modules to absolutely pure semimodules. Two subclasses of semimodules are studied: that of absolutely pure semimodules and that of finitely injective semimodules. If the semiring \(R\) is additively idempotent, then the two subclasses coincide. A characterization of Fieldhouse regular semimodules is given.
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