On Lcem Matrices Over Unique Factorization Domains

Abstract

In this paper, we extend the concept of lcem matrices beyond the classical domain of natural integers into the domain of unique factorization domains. We investigate the structure of these matrix types when applied to both arbitrary sets and gced-closed sets. Furthermore, we find the determinant, the trace and the inverse of such matrices. To simplify these ideas, we employ domains such as the Gaussian integers domain and the domain of polynomials defined over finite fields.

Keywords

• Lcem matrices
• Exponential divisor
• Unique factorization domain

References

1. Chehade, H., Awad, Y., & Zeid, W. (2024). On lcem matrices over unique factorization domains. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 62-72.