On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏

Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3292 2022 2022 On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏 Department of Mathematics, University of Rijeka, City of Rijeka, Croatia Sandra Sandra Department of Mathematics, University of Rijeka, City of Rijeka, Croatia Stipan Podobnic 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)). 2024 2024 37 43 10.54216/GJMSA.0110205 https://www.americaspg.com/articleinfo/33/show/3292