Received January 25, 2025. Published online February 23, 2026.
Abstract: The main objective of this paper is to investigate residuated EQ-algebras endowed with square roots. First, the concept of a square root on residuated EQ-algebras is introduced, and several of its properties are examined in the context of involutive, prelinear EQ-algebras and Boolean algebras. Subsequently, the notion of square filters in EQ-algebras is presented, and a one-to-one correspondence is established between the set of all square filters and the set of all square congruence relations induced by filters in good EQ-algebras. Finally, the concept of strict square roots on residuated EQ-algebras is introduced. Moreover, it is demonstrated that for a prelinear residuated EQ-algebra $E$ equipped with a strict square root, the quotient algebra $\frc{E}F $ is trivial, where $F$ is a positive implicative filter of $E$.
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Affiliations: Akbar Paad, Department of Mathematics, University of Bojnord, 4th Km Road to Esfarayen, Bojnord, North Khorasan, P. O. Box 9453155111, Bojnord, Iran and Department of Mathematics Education, Farhangian University, P. O. Box 14665-889, Teheran, Iran, e-mail: a.paad@ub.ac.ir, akbar.paad@gmail.com
