We propose a generalization of the learning parity with noise (LPN) and learning with errors (LWE) problems to an abstract class of group-theoretic learning problems that we term learning homomorphisms with noise (LHN). This class of problems contains LPN and LWE as special cases, but is much more general. It allows, for example, instantiations based on non-abelian groups, resulting in a new av...

Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. In this paper we define and study the commutative pseudo equality algebras. We give a characterization of commutative pseudo equality algebras and we prove that an invariant pseudo equa...

It is shown in first order perturbation theory that anharmonic oscillators in non-commutative space behave smoothly in the commutative limit just as harmonic oscillators do. The non-commutativity provides a method for converting a problem in degenerate perturbation theory to a non-degenerate problem. In the last few years theories in non-commutative space [1]-[5] have been studied extensively. ...

Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties of $Gamma(R)$ are studied. We investigate connectivity and the girth of $Gamma(R)$, where $...