FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

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 when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

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 (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

ON THE RADICAL OF A FREE MALCEV ALGEBRA

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 the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

Algebras determined by their supports

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander-Reiten components of an ada algebra which is not quasi-tilted, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes. (C) 2011 Elsevier B.V. All rights reserved.

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.

The influence of asthma onset and severity on malocclusion prevalence in children and adolescents

OBJECTIVE: The influence of asthma, its severity levels and onset time on malocclusion occurrence were investigated. METHODS: The sample was composed by 176 children/adolescents, of both genders, aged 3 to 15 years, that were divided in two groups. The asthma group (AG) enrolled 88 children/adolescents that were seen at the Breathe Londrina Program. The asthma-free group (AFG) enrolled 88 preschool and school children recruited in 2 public schools. Malocclusion diagnosis was made according to WHO criteria (OMS, 1999). RESULTS: A higher prevalence in malocclusions in asthmatic patients in mixed dentition was observed when compared to controls (p<0.05). On the other hand, these results were not observed for deciduous (p>0.05) and permanent dentition (p>0.05). A significant association was seen between asthma onset time and marked maxillary overjet (p<0.05), and open bite (p<0.05) in the mixed dentition, being both conditions more common among those that have presented the symptoms of asthma prior to 12 months of age. CONCLUSION: The results of this study indicate that the early manifestation of asthma at first year of life can cause dentofacial changes. Therefore, the prompt diagnostic of the illness, as well as the establishment of a proper therapy could improve the symptoms and chronic complications of asthma and also reduce its impact on craniofacial development.

Food Competition in a Semi-Free-Ranging Cebus apella Group

The competitive regime faced by individuals is fundamental to modelling the evolution of social organization. In this paper, we assess the relative importance of contest and scramble food competition on the social dynamics of a provisioned semi-free-ranging Cebus apella group (n=18). Individuals competed directly for provisioned and clumped foods. Effects of indirect competition were apparent with individuals foraging in different areas and with increased group dispersion during periods of low food abundance. We suggest that both forms of competition can act simultaneously and to some extent synergistically in their influence on social dynamics; the combination of social and ecological opportunities for competition and how those opportunities are exploited both influence the nature of the relationships within social groups of primates and underlie the evolved social structure. Copyright (c) 2008 S. Karger AG, Basel

A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.

Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

Does group size matter? Cheating and cooperation in Brazilian school children

Cooperation between individuals is an important requisite for the maintenance of social relationships. The purpose of this study was to investigate cooperation in children in the school environment, where individuals could cooperate or not with their classmates in a public goods game. We investigated which of the following variables influenced cooperation in children: sex, group size, and information on the number of sessions. Group size was the only factor to significantly affect cooperation, with small-group children cooperating significantly more than those in large groups. Both sex and information had no effect on cooperation. We suggest that these results reflect the fact that, in small groups, individuals were more efficient in controlling and retaliating theirs peers than in large groups. (C) 2008 Elsevier Inc. All rights reserved.

Normal Enveloping Algebras

A full characterization is given of ordinary and restricted enveloping algebras which are normal with respect to the principal involution.

Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.

Generalizations of Lie Algebras

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 influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.