Thesis (doctoral)--Königl. Bayer. Julius-Maximilians-Universität Würzburg, 1911. / Vita. Includes bibliographical references.

Inaug.-diss.--Universität Marburg, 1915. / Lebenslauf. "Literaturnachweis": p. [3]

Inaug.-diss.--Bern. / Lebenslauf. "Quellen": 2d prelim. leaf.

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Let X be a fixed Banach space, S a scalar type operator in B(X), and G a complex polynomial in two indeterminates. The aim of this thesis is to characterize all operators T ∊ B(X) which commute with S and satisfy the algebraic equation G(S,T) = 0. / Science, Faculty of / Mathematics, Department of / Graduate

published_or_final_version / Mathematics / Master / Master of Philosophy

We define a formula (phi)(x;t)(' )in a first-order language L, to be an equation in a category of L-structures if, for any H in , and set p = {(phi)(x;a(,i));(' )i (ELEM) I, a(,i)(' )(ELEM) H} there is a finite set I(,0) (L-HOOK) I such that for any f:H(--->)F in ,(' )(INTERSECT)(,i(ELEM)I(,0))(phi)(F;fa(,i)) =(' )(INTERSECT)(,i(ELEM)I)(phi)(F;fa(,i)). / We say that a complete theory T is equational if any formula is equivalent in T to a boolean combination of equations in od(T), and we note that equational theories are stable. / Thus, we develop a theory of independence with respect to equations in general categories of structures, which is similar to the one introduced in stability (and actually identical to it in the case of equational theories) but which, in our context, have an algebraic character. / We then compare the concepts introduced in stability theory to corresponding notions in the context of equational theories.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 22, 2009) Vita. Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1990.