Reciprocal Power GCDQ Matrices and Power LCMQ Matrices Defined on Factor Closed Sets over Euclidean Domains

Abstract

In this paper, we use a generalization for the Jordan totient function over Euclidean domains to give a full generalization of the Reciprocal Power GCDQ Matrices and Power LCMQ Matrices. Their structures, determinants defined on arbitrary and factor-closed q-ordered sets are studied over Euclidean domains. In addition, precedents demonstrating our work are likewise given in some well-known UFDs.