En este trabajo estudiamos el álgebra de Lie asociado con la filtración de la serie central del grupo de trenzas pura de Artin y probamos que es una extensión de las álgebras de Lie libres.

Shan Chin-Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 44-45.

We study the -adic completion dD[1] of Berthelot's differential operators of level one on the projective line over a complete discrete valuation ring of mixed characteristic (0; p). The global sections are shown to be isomorphic to a Morita context whose objects are certain fractional ideals of primitive factor rings of the -adic completion of the universal enveloping algebra of sl2(R). We produce a bijection between the coadmissibly primitive ideals of the Arens Michael envelope of a nilpotent finite dimensional Lie algebra and the classical universal enveloping algebra. We make limited progress towards characterizing the primitive ideals of certain a noid enveloping algebras of nilpotent Lie algebras under restrictive conditions on the Lie algebra. We produce an isomorphism between the primitive factor rings of these affinoid enveloping algebras and matrix rings over certain deformations of Berthelot's arithmetic differential operators over the a fine line.

The move from GCSE to 'A' level mathematics in schools in England and Wales can be, at least partly, characterised by an increase in abstraction and sophistication associated with the introduction of more variables. I have described as 'second variable' situations those in which letters were used in roles that went beyond the single unknown value or the dependent and independent variable, for example - the equation y = mx + c as a general equation of a straight line - the use of (a, b) to describe a general point. This thesis attempts to describe the experiences of students in meeting these situations. The data which I present are drawn from a variety of sources, but come chiefly from a year spent teaching and observing two 'A' level mathematics classes in two different schools. Other sources are my own mathematical work and that of colleagues, in particular two groups of teachers with whom I met to discuss my research. I also refer to my teaching of other groups of students. My conclusions - distinguish between structural and empirical generalisation - identify the shifts in the roles of literal symbols which take place in the solving of some types of problem - describe how stereotyping affects students' treatment of literal symbols and assists in or interferes with solving of problems - list some components of 'second variable thinking'. My research method is qualitative rather than quantitative. It draws on my teaching experience and makes a virtue of the subjectivity of both the researcher and the reader. I offer a number of mathematical exercises to the reader and intend that he should draw on his experience of these exercises in interpreting the thesis. I expect the validity of the thesis to be judged by its coherence and by its capacity to inform the future practice of myself and of readers.

In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M12. We have given several progenitors, permutation and monomial, including 2*4:(22:3), 2*5:D10, 2*8:((4X2).D4), 3*7:m L2(7), 2*6:(Z3 wr Z2), and 2*24: (2. A5) and their homomorphic images which include 4.(M12:2), the group of automorphisms of M12 and several classical groups. We have given the isomorphism type of each of the group mentioned in the thesis. In each case, a proof of the isomorphism type is provided, either computer-based or by hand. In addition, by hand constructions, using the technique of double coset enumeration, are given for the groups L2(11)X3, L2(11), PGL2(11), S5,(A5XA5):4, A7, and 37:L2(7).

Thesis (Ph. D.)--Oregon State University, 1963. / Typescript. Includes bibliographical references (leaf 32). Also available on the World Wide Web.

The zero-divisor graph of a commutative ring is the graph whose vertices are the nonzero zero-divisors of the ring such that distinct vertices are adjacent if and only if their product is zero. We use this construction to study the interplay between ring-theoretic and graph-theoretic properties. Of particular interest are Boolean rings and commutative rings of quotients.

Thesis (Ph. D.)--University of Chicago, 1915. / Vita. "Reprinted from American journal of mathematics, vol. XXXVIII, no. 2, April, 1916." Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Universität Marburg, 1914. / "Sonderabdruck aus dem Journal für die reine und angewandte Mathematik, Bd. 145"--T.p. verso. Vita.

Thesis (Ph. D.)--University of Chicago, 1936. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Includes bibliographical references.