For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.
We study the weak hereditary class of all weak subalgebras of algebras in a total variety . We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.
Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted and , respectively). The eigenproblem is the search for a vector (an eigenvector) and a constant (an eigenvalue) such that , where is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation with given matrices and unknown constant and vector . Generalized eigenvectors have interesting...