GENERALIZED PELL EQUATIONS FOR 2 × 2 MATRICES
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 1
Abstract
In this paper we consider the solutions of the generalized matrix Pell equations X^2 − dY^2 = cI, where X and Y are 2 × 2 matrices over Z, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity matrix. We determine all solutions of such equations for c = ±1, as well as all non-commutative solutions for an arbitrary c.
Authors and Affiliations
Boaz Cohen
AN EQUATIONAL AXIOMATIZATION OF POST ALMOST DISTRIBUTIVE LATTICES
In this paper, we prove that the class of P2-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.
ON QI-ALGEBRAS
In this paper, the notion of a QI-algebra is introduced which is a generalization of a BI-algebra and there are studied its properties. We considered ideals, congruence kernels in a QI-algebra and characterized congruenc...
SEMIGROUPS DERIVED FROM (Γ, N)-SEMIHYPERGROUPS AND T-FUNCTOR
The main purpose of this paper is to introduce the concept of (Γ, n)- semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category...
Congruences and Trajectories in Planar Semimodular Lattices
A 1955 result of J. Jakub´ık states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size). The problem is how to determine whether...
WEAK-HYPERLATTICES DERIVED FROM FUZZY CONGRUENCES
In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the...