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Abstract Ideal Theory: Principals and Particulars

  • Chapter
The Dilworth Theorems

Part of the book series: Contemporary Mathematicians ((CM))

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Abstract

The subject of abstract ideal theory has developed along two more or less distinct though related lines since its beginnings in the twenties and thirties. One line involves an ideal operator x which is applied to subsets of a semigroup S to produce a lattice ordered semigroup L of ideals. The other, and the one of primary interest to us in this discussion, begins immediately with the lattice ordered semigroup L, dispensing entirely with the assumption of underlying elements.

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Author information

Authors and Affiliations

  1. The University of Iowa, Iowa City, IA, 52242, USA

    E. W. Johnson

Authors
  1. E. W. Johnson
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Dartmouth College, Hanover, NH, 03755, USA

    Kenneth P. Bogart

  2. Department of Mathematics, University of Hawaii, Honolulu, HI, 96822, USA

    Ralph Freese

  3. Department of Mathematics, University of North Texas, Denton, TX, 76203-5116, USA

    Joseph P. S. Kung

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© 1990 Springer Science+Business Media New York

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Johnson, E.W. (1990). Abstract Ideal Theory: Principals and Particulars. In: Bogart, K.P., Freese, R., Kung, J.P.S. (eds) The Dilworth Theorems. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3558-8_37

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  • DOI: https://doi.org/10.1007/978-1-4899-3558-8_37

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4899-3560-1

  • Online ISBN: 978-1-4899-3558-8

  • eBook Packages: Springer Book Archive

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