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On the Jacobson radical of a semiring.

Authors :
Bhuniya, A. K.
Sarkar, Puja
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

Subjects :
*JACOBSON radical
*RADICALS

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