R. Costa, Henrique Guzzo Jr., A. Grichkov, L.A. Peresi,

• Preface -- Contributors -- New approach to octonions and Cayley algebras /Helena Albuquerque and Shahn Majid -- Identities of graded alternative algebras /Y. Bahturin and M. Zaicev -- Invariant connections on symmetric spaces /Pilar Benito, Cristina Draper, and Alberto Elduque -- £-ideals in Bernstein algebras /A. Catalan -- Octonions and affine connections on spheres /Alberto Elduque and Hyo Chul Myung -- Immediate applications of a new classification of finite dimensional simple Lie algebras /Mohammed El Houari -- An approach to integrable theories in any dimension: the role of non-semi simple Lie algebras /Luiz A. Ferreira -- Versal deformations of Lie algebras /Alice Fialowski -- Derivations in second order Bernstein algebras /M. A. Garcia-Muniz and C. Martinez -- Algebraic structure of the non-abelian Toda models /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Alternative rings of small order and the hunt for Moufang circle loops /Edgar G. Goodaire -- A note on linearization of some identities /H. Guzzo, Jr., and P. Vicente -- The commuting nucleus of right alternative rings /Irvin Roy Hentzel -- A construction of Jordan superalgebras from Jordan-Lie triple systems /Noriaki Kamiya and Susumu Okubo -- Rings with (x,y,z) = (x,z,y) /Erwin Kleinfeld and Margaret Kleinfeld -- On the semi simplicity of special Jordan superalgebras /Carlos Gomez-Ambrosi and Jesus Laliena -- Bernstein superalgebras of dimension four /S. Gonzalez, C. Lopez-Diaz, and C. Martinez -- Banach-Bemstein algebras and their applications /Yu. Lyubich -- Jordan superalgebras /C. Martinez -- Derivations of structurable / /*-algebras /J. Martinez Moreno -- Lie mappings of C* -algebras /Martin Mathieu -- Sur des anneaux commutatifs a puissances associatives de caracteristique premiere p> 0 /Joao Carlos da Motta Ferreira and Artibano Micali -- Principal ^-bundles /Alexander I. Nesterov -- Z x Z-graded Lie algebras containing a Heisenberg algebra /J. Marshall Osborn and Kaiming Zhao -- A„(l) Toda solitons: a relation between dressing transformations and vertex operators /H. Belich and R. Paunov -- Generalized quadratic rings /Luiz Antonio Peresi -- The derivation algebra of a division composition algebra /J. M. Perez-Izquierdo -- On the structure of the simple Moufang loop GLL (F2) /M. L. Merlini Giuliani and Cesar Polcino Milies -- Lie groups, differential geometry, and nonlinear integrable systems /A V. Razumov and M. V. Saveliev -- Smooth quasigroups and loops. Recent achievements and open problems /L. V. Sabinin -- On smooth left square distributive quasigroup /Liudmila Sabinina -- Algebraic structure of trans symmetric spaces /L. V. Sbitneva -- Bernstein algebras whose lattice of ideals is distributive /C. Martinez and J. Setd -- Specialty problem for Malcev algebras and Poisson Malcev algebras /Ivan P. Shestakov -- Applications of Lie ring methods to group theory /Pavel Shumyatsky -- Computable rings, groups and their isomorphisms /Bakhadyr Khoussainov and Arkadii Slinko -- Quantum F-algebras /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Conditions d’existence d’une loi de Hardy-Weinberg periodique dans des populations selectivement neutres /C. Mallol and R. Varro -- Finite semi fields three-dimensional over the left nuclei /G. P. Wene -- Supplementing radicals of nonassociative rings /Richard Wiegandt.