NDLI: Modular and Distributive Semilattices

Content Provider	Scilit
Author	Rhodes, Joe B.
Copyright Year	1975
Description	A modular semilattice is a semilattice in which implies that there exist such that and . This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical characterizations of modular and distributive lattices by their sublattices: A semilattice is modular if and only if each pair of elements of has an upper bound in and there is no retract of isomorphic to the nonmodular five lattice. A semilattice is distributive if and only if it is modular and has no retract isomorphic to the nondistributive five lattice.
Related Links	http://www.ams.org/tran/1975-201-00/S0002-9947-1975-0351935-X/S0002-9947-1975-0351935-X.pdf
Ending Page	41
Page Count	11
Starting Page	31
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1997322
Journal	Transactions of the American Mathematical Society
Volume Number	201
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Logic Lattice Poset Distributive Ideal Modular Semilattice
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Modular and Distributive Semilattices