# On k-Noetherian and k-Artinian Semirings

## TL;DR

This paper explores the properties of left k-Noetherian and k-Artinian semirings, providing characterizations via i-injective semimodules and extending classical theorems to the semiring context.

## Contribution

It introduces new characterizations of k-Noetherian and k-Artinian semirings using i-injective semimodules and presents a partial version of the Bass-Papp Theorem for semirings.

## Key findings

- Characterization of k-Noetherian and k-Artinian semirings
- Extension of Bass-Papp Theorem to semirings
- Examples and counterexamples illustrating main results

## Abstract

We investigate left k-Noetherian and left k-Artinian semirings. We characterize such semirings using i-injective semimodules. We prove in particular, a partial version of the celebrated Bass-Papp Theorem for semiring. We illustrate our main results by examples and counter examples.