Mohammed, A. and Ahmed, B. M.2025-05-082025-05-0820219. Mohammed, A. and Ahmed, B. M. (2021): Boolean Ring With Underlying Power Rhotrix Set, Katsina Journal of Natural and Applied Sciences, 10(2), 130 -138, Published by Umaru Musa Yar’adua University, Katsina State, Nigeria.2141- 0755https://uilspace.unilorin.edu.ng/handle/123456789/16396This paper introduces 'the notion of power rhotrix set ring' and its method of construction . This ring is a form of Boolean ring which uses operations of symmetric difference and intersection for addition and multiplication respectively. The basic properties of the power rhotrix set ring are discussed and a number of its subrings are uncovered. It is hope this idea would serve as foundation for extending many other concepts in ring theory to power rhotrix set ring theory.enRingrhotrix set ringpower rhotrix set ringBoolean ring