Selected Papers

Saunders Mac Lane, Irving Kaplansky (Autoren)

Buch | Softcover

572 Seiten

2012 | Softcover reprint of the original 1st ed. 1979
Springer-Verlag New York Inc.
978-1-4615-7833-8 (ISBN)

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Saunders Mac Lane was an extraordinary mathematician and a dedicated teacher, who cared deeply about the values of science and education. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Gottingen. He studied under David Hilbert, Hermann Weyl, and Paul Bernays. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

[2]* Abgekurzte Beweise im Logikkalkul.- A Late Return to a Thesis in Logic.- [10] A construction for absolute values in polynomial rings.- [11] A combinatorial condition for planar graphs.- [13] Planar graphs whose homeomorphisms can all be extended for any mapping on the sphere.- [14] A lattice formulation for transcendence degrees and p-bases.- [21] Modular fields, I. Separating transcendence bases.- [22] Subfields and automorphism groups of p-adic fields.- [28] Note on the relative structure of p-adic fields.- [41] Group extensions and homology.- [44] Groups of algebras over an algebraic number field.- [45] Relations between homology and homotopy groups.- [48] General theory of natural equivalences.- [55] Groups, categories and duality.- [58] Cohomology theory in abstract groups, III. Operator homomorphisms of kernels.- [63] On the 3-type of a complex.- [69] Acyclic models.- [78] Homologie des anneaux et des modules.- [90] Natural associativity and commutativity.- [105] The Milgram bar construction as a tensor product of functors.- [107] Hamiltonian mechanics and geometry.- [109] Coherence in closed categories.- Saunders Mac Lane as a Shaper of Mathematics and Mathematicians.- The Early Work of Saunders Mac Lane on Valuations and Fields.- Some Remarks on the Interface of Algebra and Geometry.- Saunders Mac Lane and Category Theory.- Bibliography of the Publications of Saunders Mac Lane.- List of Ph.D. Theses written under the Supervision of Saunders Mac Lane.

Zusatzinfo	biography
Verlagsort	New York, NY
Sprache	englisch
Maße	170 x 244 mm
Gewicht	973 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Schlagworte	Algebra • MacLane, Saunders
ISBN-10	1-4615-7833-7 / 1461578337
ISBN-13	978-1-4615-7833-8 / 9781461578338
Zustand	Neuware