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In this paper, we explore locally principal element lattices in terms of primary, semiprimary and prime power elements.

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Let be aC-lattice which is strong join principally generated. In this paper, we consider prime elements of 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 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 , then is the finite direct product of one-dimensional domains and primary lattices.

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Acta Mathematica Hungarica
E. W. Johnson
J. A. Johnson
, and
M. B. Taylor
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