ISSN:
1420-8911
Keywords:
06F10
;
06F99
;
13A15
;
multiplicative lattices
;
Noether lattice
;
principal element
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01236764
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