# On Semisimple Semirings

## TL;DR

This paper explores the properties of ideal-semisimple and congruence-semisimple semirings, providing new characterizations and extending classical ring results to broader semiring classes.

## Contribution

It introduces novel characterizations of semisimple semirings using e-projective and e-injective semimodules, extending known ring results to non-subtractive commutative semirings.

## Key findings

- New characterizations of semisimple semirings
- Extension of ring semisimplicity results to semirings
- Broader understanding of semiring structures

## Abstract

We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not necessarily subtractive) commutative semirings.