POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

The Usefulness of Caries Frequency, Depth, and Location in Determining Cariogenicity and Past Subsistence: A Test on Early and Later Agriculturalists From the Peruvian Coast

Dental markers have been used to unravel particularities of paleodiet, subsistence, social structure, and health. This article aims to compare oral pathology among four pre-Columbian groups with different degrees of agricultural and socio-cultural development but comparable ecological conditions who lived on the coastal desert of Peru. Three of these groups are assigned to distinct phases of the Formative Period (2500-1 BC), a time critical for our understanding of the development of agriculture and social complexity. The fourth group corresponds to the Late Intermediate Period (1000-1470 AD), when agriculture had its apogee and society was highly stratified. In this study we test whether there is an increase (1) in the frequency of carious lesions and (2) in caries depth, and (3) if there is a shift from occlusal to extra-occlusal caries locations with the development of agriculture. Therefore, we analyze the frequencies of carious lesions and antemortem tooth loss (AMTL), the caries distributions by age, sex, and type of tooth, as well as the tissues affected by, and the location of the carious lesions. Since there are no significant differences in the frequencies of carious lesions and AMTL between the groups, we reject hypothesis 1. In contrast, caries depth does increase, and caries location changes from occlusal to extra-occlusal sites with agricultural development. However, we can only corroborate hypothesis 2 and 3 when taking into consideration dental wear. Thus, we recommend that caries depth and locations should be used with evaluations of dental wear to reconstruct subsistence in ancient populations. Am J Phys Anthropol 143:75-91, 2010. (C) 2010 Wiley-Liss, Inc.

Neuropsychological Assessment of Current and Past Crack Cocaine Users

Background: Cognitive changes due to crack cocaine consumption remain unclear Methods: For clarification, 55 subjects were assigned to three groups: control group, crack cocaine current users, and ex-users. Participants were submitted to Mini-Mental State Examination (MMSE) and tasks evaluating executive functioning and verbal memory Mood state was also measured. Intergroup comparisons were carried out. Results: Control group performance on the MMSE was better than that of users and ex-users. Verbal memory performance for logical memory of users was impaired. Ex-users scored lower on DSST and Trail Making Test (Part B). Conclusion: Chronic crack cocaine use seems to disrupt general cognitive functioning (MMSE), verbal memory, and attentional resources, but findings suggest that some of these effects could be reversed by abstinence.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.