Primary units in cyclotomic fields

TL;DR

This paper explores the relationships between different types of primary units in local cyclotomic fields and their connection to global units, enhancing understanding of algebraic number theory structures.

Contribution

It provides new insights into the interrelations of primary units in local cyclotomic fields and their links to global units, clarifying their algebraic properties.

Findings

Identifies key relationships among primary units in local cyclotomic fields.

Establishes connections between local primary units and global units.

Advances theoretical understanding of cyclotomic field structures.

Abstract

We investigate the interrelationships of three notions of primary units in the local cyclotomic field of $p$-th roots of~1($p$ being an odd prime number), especially with reference to global units.