Noetherian ring with free additive groups

TL;DR

This paper demonstrates the existence of Noetherian rings, specifically domains, with free additive groups across all infinite cardinalities, expanding previous results in algebra.

Contribution

It establishes the existence of Noetherian rings with free additive groups for every infinite cardinality, extending earlier work in the field.

Findings

Existence of Noetherian domains with free additive groups in all infinite cardinalities

Generalization of previous algebraic constructions

Expansion of known classes of rings with specific additive group properties

Abstract

There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)