# Pseudocomplementation and Minimal Prime Ideals in Semirings

## TL;DR

This paper introduces pseudocomplementation in semirings, explores minimal prime ideals, and generalizes classical ring theory results to semirings, expanding the algebraic framework.

## Contribution

It presents the novel concept of pseudocomplementation in semirings and extends classical minimal prime ideal results from ring theory to semiring structures.

## Key findings

- Defined pseudocomplementation for semirings
- Proved properties of minimal prime ideals in semirings
- Generalized classical ring results to semiring context

## Abstract

In the first section of the present work, we introduce the concept of pseudocomplementation for semirings and show semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some interesting results for minimal prime ideals of such semirings. In the second section, some classical results for minimal prime ideals in ring theory are generalized in the context of semiring theory.