Work

Finite Local Rings of Length 4

Year: 2024

Type: article

Abstract: This paper presents a comprehensive characterization of finite local rings of length 4 and with residue field Fpm, where p is a prime number. Such rings have an order of p4m elements. The current paper provides the structure and classification, up to isomorphism, of local rings consisting of p4m elements. We also give the exact number of non-isomorphic classes of these rings with fixed invariants p,n,m,k. In particular, we have listed all finite local rings of 4-length and of order p8 and 256.

Source: Axioms

DOI: 10.3390/axioms14010012

Authors: Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori

Institutions: King Saud University, Dr. Babasaheb Ambedkar Marathwada University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: King Saud University