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Varieties of Algebras whose Congruence Lattices Satisfy Lattice Identities


Nation, James Bryant (1973) Varieties of Algebras whose Congruence Lattices Satisfy Lattice Identities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SQ79-4T38.


Given a variety K of algebras, among the interesting questions we can ask about the members of K is the following: does there exist a lattice identity S such that for each algebra A ε K, the congruence lattice ϴ(A) satisfies S ? This thesis deals with questions of this type.

First, the thesis shows that the congruence lattices of relatively free unary algebras satisfy no nontrivial lattice identities.

It is also shown that the class of congruence lattices of semi-lattices satisfies no nontrivial lattice identities. As a consequence it is shown that if K is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of K are groups with exponent dividing a fixed finite number. In particular, the congruence lattices of members of K are modular

Finally, it is shown that the varieties whose congruence lattices satisfy one of a class of lattice identities of a fairly general form are in fact congruence modular.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dilworth, Robert P.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 May 1973
Funding AgencyGrant Number
Ford FoundationUNSPECIFIED
Record Number:CaltechTHESIS:01312018-090230596
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10658
Deposited By: Benjamin Perez
Deposited On:31 Jan 2018 18:59
Last Modified:21 Dec 2019 04:12

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