GEOMETRIES Jaroslav Ježek First edition , April 2008

Universal Algebra

Enumerating Left Distributive Groupoids

Groupoids satisfying the equation x(yz) = (xy)(xz) are called left distributive, or LD-groupoids. We give an algorithm for their enumeration and prove several results on the collection of LD-groupoids extending a given monounary algebra.

Some Decidable Congruences of Free Monoids

Let W be the free monoid over a finite alphabet A. We prove that a congruence of W generated by a finite number of pairs 〈au, u〉, where a ∈ A and u ∈ W , is always decidable.

Commutative Semigroups That Are Nil of Index 2 and Have No Irreducible Elements

Every commutative nil-semigroup of index 2 can be imbedded into such a semigroup without irreducible elements.

H2O2-Activated Mitochondrial Phospholipase iPLA2γ Prevents Lipotoxic Oxidative Stress in Synergy with UCP2, Amplifies Signaling via G-Protein–Coupled Receptor GPR40, and Regulates Insulin Secretion in Pancreatic β-Cells