Research Article Kernel L-Ideals and L-Congruence on a Subclass of Ockham Algebras Teferi Getachew Alemayehu , 1 Derso Abeje Engidaw , 2 and Gezahagne Mulat Addis 2 1 Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia 2 Department of Mathematics, University of Gondar, Gondar, Ethiopia Correspondence should be addressed to Teferi Getachew Alemayehu; teferigetachew3@gmail.com Received 26 January 2022; Accepted 12 April 2022; Published 29 May 2022 Academic Editor: Tareq Al-shami Copyright © 2022 Teferi Getachew Alemayehu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we study L-congruences and their kernel in a subclass K n,0 of the variety of Ockham algebras A. We prove that the class of kernel L-ideals of an Ockham algebra forms a complete Heyting algebra. Moreover, for a given kernel L-ideal ξ on A, we obtain the least and the largest L-congruences on A having ξ as its kernel. 1. Introduction e concept of an Ockham algebra was first introduced by Berman [1], in 1977. Next, it has been studied by Urquhart et al. [2], Goldberg et al. [3, 4], and Blyth and Varlet [5]. Blyth and Silva [5] presented the concept of kernel ideals in Ockham algebra. Wang et al. [6] presented Congruences and kernel ideals on a subclass K n,0 of the variety of Ockham Algebras (in which h 2n  id A ). e varieties of Boolean al- gebras, De Morgan algebras, Kleene algebras, and Stone algebras are some of the well-known subvarieties of Ockham algebra. We see [7] for the basic concepts of the class of Ockham algebras. On the other side, for the first time, the concept of fuzzy sets was presented by Zadeh as an extension of the classical notion of set theory [8]. He defined a fuzzy subset of a nonempty set K as a function from K to [0, 1]. Goguen in [9] presented the notion of L-fuzzy subsets by replacing the interval [0, 1] with a complete lattice L in the definition of fuzzy subsets. Swamy and Swamy [10] studied that complete lattices that fulfill the infinite meet distributive law are the most appropriate candidates to have the truth values of general fuzzy statements. e study of fuzzy subalgebras of different algebraic structures has been begun after Rosenfeld presented his paper [11] on fuzzy subgroups. is paper has provided sufficient motivation to researchers to study the fuzzy subalgebras of different algebraic structures. Fuzzy congruence relations on algebraic structures are fuzzy equivalence relations that are compatible (in a fuzzy sense) with all fundamental operations of the algebra. e concept of fuzzy congruence relations was presented in different algebraic structure: in semigroups (see [12, 13]), in groups, semirings, and rings (see [14–19]), in modules and vector spaces (see [20, 21]), in lattices (see [22, 23]), in universal algebras (see [24, 25]), and more recently in MS- algebras and Ockham Algebras (see [26–28]). Initiated by the above results, we present Kernel L-ideals and L-Congruence on a subclass FI k (A) of K n,0 of the variety of Ockham algebras and study their characteristics. We prove that the class of kernel L-ideal LI k (A) of K n,0 -algebra A forms Heyting algebras. Also, we get the least and the biggest L-congruences, respectively, on K n,0 -algebra A having a given L-ideal as an L-kernel. 2. Preliminaries is section contains basic definitions and important results which will be used in the sequel. Definition 1. (see [5]). An algebra (A; ∧, ∨, h, 0, 1) of type (2, 2, 1, 0, 0) is said to be an Ockham algebra if Hindawi Journal of Mathematics Volume 2022, Article ID 7668044, 9 pages https://doi.org/10.1155/2022/7668044