# Some remarks on $K_0$ of noncommutative tori

## TL;DR

This paper constructs generators for the K_0 groups of all noncommutative tori by utilizing Rieffel's projective modules and a continuous field approach, advancing the understanding of their K-theoretic structure.

## Contribution

It introduces a method to generate K_0 groups of noncommutative tori using projective modules over continuous fields, extending previous results.

## Key findings

- Constructed projective modules over continuous fields of noncommutative tori.
- Provided generators for K_0 groups of all noncommutative tori.
- Connected Rieffel's modules with K-theoretic invariants.

## Abstract

Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibers are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of $K_0$ of all noncommutative tori.