1. On the Jacobson radical and semisimplicity of a semiring
- Author
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Bhuniya, A. K. and Sarkar, Puja
- Subjects
Rings and Algebras (math.RA) ,FOS: Mathematics ,Mathematics - Rings and Algebras ,16Y60, 16N99, 16D99 - Abstract
Based on the minimal and simple representations, we introduce two Jacobson-type Hoehnke radicals, m-radical and s-radical, of a semiring $S$. Every minimal (simple) $S$-semimodule is a quotient of $S$ by a regular right congruence (maximal) $\mu$ on $S$ such that $[0]_\mu$ is a maximal $\mu$-saturated right ideal in $S$. Thus the m(s)-radical becomes an intersection of some regular congruences. Finally, every semisimple semiring is characterized as a subdirect product of primitive semirings; and every s-primitive semiring is represented as a 1-fold transitive subsemiring of the semiring of all endomorphisms on a semimodule over a division semiring.
- Published
- 2023
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