MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued ...

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be ...

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev ...

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an ...

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case ...

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from ...

In this paper, we show that free algebras in the variety of residuated lattices and some of its subvarieties are directly indecomposable and show, as a consequence, the direct indecomposability of free algebras for some ...

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been ...

In Juriaans et al. (2009) [9] we constructed pairs of units u,v in Z-orders of a quaternion algebra over View the MathML source, d a positive and square free integer with View the MathML source, such that 〈un,vn〉 is free ...