Composites In Semirings of Boolean Groups

TL;DR

This paper estimates the quantity of composite elements in the semiring of finite boolean groups, suggesting that composites in the semiring of finite groups are sparsely distributed.

Contribution

It introduces an estimation method for composite elements in the group semiring of boolean groups and conjectures about their distribution.

Findings

Number of composite elements estimated in boolean group semirings.

Composites in finite group semirings are likely sparsely dispersed.

Provides a new perspective on the structure of group semirings.

Abstract

We estimate the number of composite elements in the $n$-th grade of the group semiring of finite boolean groups. In view of this result we may conjecture that the composites in the semiring of finite groups are thinly dispersed.