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.

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.

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

ASSOCIATIVE IDENTITIES OF OCTONIONS

We work to find a basis of identities for an octonion algebra modulo an associator ideal of a free alternative algebra, or, in other words, a basis for an associative replica of an ideal of identities of an octonion algebra.

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.

Alternative Identities and Foreign Language Learning

My D-essay has the working title “Alternative Identities and Foreign Language Learning”. I have chosen this area because I have noticed a certain reluctance among Swedish students to use the foreign language English in English classes. They often seem embarrassed to express themselves in a language which is not their mother tongue, but they seem less embarrassed when they are allowed to act somebody else. These two observations converge into a focus of discussion on the matter, which will be supported by a minor study of my own, by extracts from other people’s essays on the matter, and by an overview of current litterature on language, identity and drama.The aim of my essay is to compare Swedish students’ willingness to use the foreign language English when acting minor plays in school, as themselves and as a chosen character, and to investigate the possibility of improving students’ willingness to use a foreign language, when given the opportunity to do so through acting somebody else.

"I'm still here. Sort of." : Constructed Identities in Paul Auster's City of Glass

Paul Auster’s City of Glass contains a jumble of identities. In fact, the identities are more numerous than the characters, and consequently, characters have several different identities. Some of these identities are obvious constructs, but with others the degree of construction is less evident. Poststructuralist theory, however, puts forward the idea that these seemingly original identities are in fact constructs to the same level as all others. Thus, this essay argues that there are no original identities; identities are constructed by outer factors. This essay discusses three outer factors contributing to the construction of identities, factors commonly discussed in poststructuralist criticism, these three being language, cultural codes and chance.

Constructing meanings and identities in child protection practice

Examines a contemporary and contentious social problem, child maltreatment, and the policy and practice in response to it, child protection.

Corners, squares and urban identities: perceptions, attitudes and values

In February 2000, the new Victorian Labor Government announced that they were removing the western shard from Lab Architecture Studio's winning Melbourne Federation Square design. then under construction. The specific 'contested terrain' at the intersection of Flinders Street and Swanston Street Walk. Melbourne, allows the exploration of the politics of place construction over time, through an examination of Young and Jackson's Hotel [1861]. St Paul's Cathedral [1886). Flinders Street Station [1912]. the Westin Hotel [1999) and Federation Square. This site brings together architectural and social history, questions public space and identity, and looks at Melburnian's perceptions, attitudes and values. It further demonstrates that the fragmentation of the professions, and fragmentary histories. lead to the preservation of 'bits' of architecture and the destruction of the urban/landscape context, jeopardizing the Identity of place.

Constructing the identities of `responsible mothers, invisible men` in child protection practice

Social constructionism offers valuable insights into the study of social problems for example, poverty, homelessness, crime and delinquency, including how social phenomena 'become' social problems, through social processes of interaction and interpretation. The social construction of child maltreatment has recently emerged as a site of scholarly inquiry and critique. This paper explores through three case studies how 'responsibility for child maltreatment' is constructed in child protection practice, with a specific focus on how 'responsibility' may also be gendered. In particular, how is gender associated with responsibility, such that the identity-pair, 'responsible mothers, invisible men', is a highly likely outcome as claimed in feminist literature? What other assumptions about 'identities of risk' or 'dangerousness' articulate with patriarchy and influence how responsibility is constructed? The case studies explore normally invisible processes by which social categories become 'fact', 'knowledge' and 'truth'. Furthermore, the social construction of 'responsibility for child maltreatment' is extended by a reflexive analysis of my own constructionist practices, as researcher/writer in claims making. The analysis offers an insight into the dynamic and dialectical relationship between professional and organisational knowledge and practice, allowing for a critique of knowledge itself, the basis for the claims made and possible alternative ways of knowing.

Caught up in the teaching-training divide: confusing professional identities

The adult education sector in Australia has undergone significant changes in recent years including a shift towards the marketisation of education and the delivery of highly prescriptive Vocational Education and Training (VET). This article reports on research that explored the ways in which educators in the adult sector understand their work and identify as professionals in this changed context. The findings of the study suggest that educators who have work histories as “teachers” strongly resist the ways in which the current discourses of VET position them as “trainers”. Data from interviews with educators and observations of them at work are analysed to highlight the ways in which they understand teaching and training as binary opposites. I examine the consequences of teachers investing in a rigid and  uncompromising teaching/training binary and argue that it is counterproductive to their forging new identities in a changed education context.

One career, two identities : an assessment of gay men`s career trajectory

Most of the research on career development of sexual minorities focuses on lesbians. Gay men, on the other hand, have received little attention in the literature as it is assumed that they face fewer difficulties in career development because they are men. This paper redresses this gap by presenting an analysis of the impact of sexual identity on the career development of gay men, drawing on both a literature review of the literature on sexual identity, gay organizational studies and career development and the results of a recent interview study. In accord with other literature, the study demonstrates that gay men, like other sexual minorities, are confronted with a conflict between personal and career needs, and have to deal with society's expectations and intolerance towards homosexuality. Suggestions are given for research that will lead to a deeper understanding of the career decisions and attitudes of gay men.