Abstract
This paper is dedicated to studying the group of units problem of the non-commutative logical extension of two different rings 𝑍𝑝 and 𝑍2𝑛, where we classify the group of units of these rings as semi-direct products of well-known abelian groups as follows: 𝑈(𝑁𝐶𝑅)𝑍𝑝≅𝑍𝑃−1∝(𝑍𝑃∝𝑍𝑃−1)𝑈(𝑁𝐶𝑅)2𝑛≅(𝑍2×𝑍2𝑛−2)⋉(𝑍2𝑛⋉(𝑍2×𝑍2𝑛−2)).
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