# On the generators of Nil $K$-groups

## TL;DR

This paper investigates the structure of higher Nil K-groups by explicitly describing their generators using binary complexes, advancing the understanding of their algebraic properties.

## Contribution

It provides an explicit description of generators for higher Nil K-groups through the use of binary complexes, a novel approach in the field.

## Key findings

- Explicit generators for higher Nil K-groups are constructed.
- Binary complexes serve as a tool to understand Nil K-groups.
- The approach clarifies the algebraic structure of Nil K-groups.

## Abstract

In this article, we study higher Nil $K$-groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$-groups in terms of binary complexes.