Journal article
Dilworth's principal elements
Algebra universalis, Vol.36(3), pp.392-404
09/1996
DOI: 10.1007/BF01236764
Abstract
Principal elements were introduced in multiplicative lattices by R. P. Dilworth, following an earlier but less successful attempt in the joint work of Ward and Dilworth. As suggested by their name, principal elements are the analogue in multiplicative lattices of principal ideals in (commutative) rings. Principal elements are the cornerstone on which the theory of multiplicative lattices and abstract ideal theory now largely rests. In this paper, we obtain some new results regarding principal elements and extend some others. In addition, we try to convey what is known and what is not known about the subject. We conclude with a fairly extensive (but likely not exhaustive) bibliography on principal elements.
Details
- Title: Subtitle
- Dilworth's principal elements
- Creators
- D. D AndersonE. W Johnson
- Resource Type
- Journal article
- Publication Details
- Algebra universalis, Vol.36(3), pp.392-404
- DOI
- 10.1007/BF01236764
- ISSN
- 0002-5240
- eISSN
- 1420-8911
- Language
- English
- Date published
- 09/1996
- Academic Unit
- Mathematics
- Record Identifier
- 9983985840702771
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