# Tensor product of dimension effect algebras

## TL;DR

This paper proves that the tensor product of dimension effect algebras results in a new dimension effect algebra, corresponding to the tensor product of their underlying dimension groups, advancing the algebraic understanding of these structures.

## Contribution

It establishes that the tensor product of dimension effect algebras remains within the class, linking it to tensor products of their associated dimension groups.

## Key findings

- Tensor product of dimension effect algebras is a dimension effect algebra.
- The tensor product corresponds to the unit interval in the tensor product of dimension groups.
- Supports algebraic structure preservation under tensor operations.

## Abstract

Dimension effect algebras were introduced in (A. Jencova, S. Pulmannova, Rep. Math. Phys. 62 (2008), 205-218), and it was proved that they are unit intervals in dimension groups. We prove that the effect algebra tensor product of dimension effect algebras is a dimension effect algebra, which is the unit interval in the unital abelian po-groups tensor product of the corresponding dimension groups.