Selected Papers and Other Writings
It is not often that one gets to write a preface to a collection of one's own papers. The most urgent task is to thank the people who made this book possible. That means first of all Hy Bass who, on behalf of Springer-Verlag, approached me about the idea. The late Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim helped in an important way; and Ina Lindemann saw the project through with tact and skill that I deeply appreciate. My wishes have been indulged in two ways. First, I was allowed to follow up each selected paper with an afterthought. Back in my student days I became aware of the Gesammelte Mathematische Werke of Dedekind, edited by Fricke, Noether, and Ore. I was impressed by the editors' notes that followed most of the papers and found them very usefuL A more direct model was furnished by the collected papers of Lars Ahlfors, in which the author himself supplied afterthoughts for each paper or group of papers. These were tough acts to follow, but I hope that some readers will find at least some of my afterthoughts interesting. Second, I was permitted to add eight previously unpublished items. My model here, to a certain extent, was the charming little book, A Mathematician's Miscel lany by J. E. Littlewood. In picking these eight I had quite a selection to make -from fourteen loose-leaf notebooks of such writings. Here again I hope that at least some will be found to be of interest.
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Abelian groups Afterthought algebraic algebras Amer annihilator assume binary quadratic forms C*-algebra central characteristic closed closure commutative complement complete modular lattice completely mixed composition series contains continuous functions continuous geometry contradiction corollary countable Dedekind ring defined direct sum direct summand division ring equivalent exists finite number finite-dimensional Hausdorff space Hence Hilbert space homomorphic hypothesis idempotents infinite integral domain invertible irreducible IRVING KAPLANSKY isomorphic Jacobson Lemma Lie algebras linear locally compact locally compact rings mapping Math Mathematical matrix maximal ideals maximal right ideal modular lattice multiplication neighborhood nilpotent nonzero orthocomplemented orthogonal projections pairs paper polynomial identity prime ideal primitive proof of Theorem prove pseudo-convergent quasi-inverse quotient field R-module rank regular maximal right representation result root self-adjoint element semi-simple structure space subalgebra submodule subring subset superalgebras Suppose Theorem theory topological ring torsion torsion-free two-sided ideal unique unit element valuation ring vanishing write