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On the Jacobson radical of a semiring.
- Source :
-
Journal of Algebra & Its Applications . Aug2024, p1. 14p. - Publication Year :
- 2024
-
Abstract
- Based on the minimal and simple representations of semirings, we introduce two Jacobson-type Hoehnke radicals, namely, <italic>m</italic>-radical and <italic>s</italic>-radical, of a semiring S. Every minimal (simple) S-semimodule is a quotient of S by a regular right congruence (maximal) μ on S such that [0]μ is a maximal μ-saturated right ideal in S. Thus the <italic>m</italic>(<italic>s</italic>)-radical becomes an intersection of a class of regular congruences. The <italic>m</italic>(<italic>s</italic>)-radical of the direct product of two semirings is the product of their individual m(s)-radicals. [ABSTRACT FROM AUTHOR]
- Subjects :
- *JACOBSON radical
*RADICALS
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 179313661
- Full Text :
- https://doi.org/10.1142/s0219498825503694