ISSN:
1588-2829
Keywords:
Primary 06F99
;
506E99
;
Multiplicative lattices
;
primary
;
semiprimary
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $$\mathcal{L}$$ be aC-lattice which is strong join principally generated. In this paper, we consider prime elements of $$\mathcal{L}$$ for which every semiprimary element is primary. We show, for example, that a compact nonmaximal primep with this property is principal. We also show that if every primep≤m has this property, then $$\mathcal{L}_m $$ is either a one dimensional domain or a primary lattice. It follows that if every primep satisfies the property, and if there are only a finite number of minimal primes in $$\mathcal{L}$$ , then $$\mathcal{L}$$ is the finite direct product of one-dimensional domains and primary lattices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01882195
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