On semimodules and Jacobson radical class. (Q2904144)
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scientific article; zbMATH DE number 6063602
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On semimodules and Jacobson radical class. |
scientific article; zbMATH DE number 6063602 |
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6 August 2012
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semirings
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radical classes
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regular classes
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special classes
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Jacobson radical
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0.9298651
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0.9140414
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0.9133702
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On semimodules and Jacobson radical class. (English)
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Using the concept of radical classes introduced by \textit{B. Morak} [Beitr. Algebra Geom. 40, No. 2, 533-549 (1999; Zbl 0962.16032)], the authors prove that any class of semirings having no nonzero homomorphic images in a regular class of semirings is a radical class. In this way they establish that the class of semirings \(A\) for which a special class of semimodules characterized inside the paper contains a faithful semimodule is regular. Then one can obtain a description of the Jacobson radical in terms of semimodules.
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