# Expansions of finite algebras and their congruence lattices

@article{DeMeo2012ExpansionsOF, title={Expansions of finite algebras and their congruence lattices}, author={William DeMeo}, journal={Algebra universalis}, year={2012}, volume={69}, pages={257-278} }

In this paper, we present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a finite algebra $${\langle B_0, \ldots \rangle}$$, let $${B_1,B_2, \ldots , B_K}$$ be sets that either intersect B0 or intersect each other at certain points. We construct an overalgebra$${\langle A, FA \rangle}$$, by which we mean an expansion of $${\langle B_0, \ldots \rangle}$$ with universe $${A = B_0 \cup B_1 \cup \ldots \cup B_K}$$, and a…

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## References

SHOWING 1-10 OF 20 REFERENCES

### Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups

- Mathematics
- 1980

I t is well-known that every algebraic lattice is isomorphic to the congruence lattice of an algebra. In this pape r we are interested in the prob lem of characterizing the finite lattices, which are…

### A constructive approach to the finite congruence lattice representation problem

- Mathematics, Computer Science
- 2000

Methods by which to construct new representable lattices from known ones are developed, and it is shown that if an order polynomially complete lattice is representable then so is every one of its diagonal subdirect powers.

### Finite forbidden lattices

- Mathematics
- 1983

Let L be any finite simple lattice of at least three elements, whose co-atoms intersect to 0. One principal result of the paper is that L is not dual isomorphic to the lattice of subvarieties of any…

### On intervals in subgroup lattices of finite groups

- Mathematics
- 2008

We investigate the question of which finite lattices L are isomorphic to the lattice [H,G] of all overgroups of a subgroup H in a finite group G. We show that the structure of G is highly restricted…

### Every Finite Lattice Can Be Embedded in a Finite Partition Lattice

- Mathematics
- 2006

We give here a proof of the theorem stated in the title. The theorem was conjectured by P. M. Whitman in [11]. The proof, mostly of combinatorial character, is based on " the regraph power technique"…

### Groups '93 Galway/St Andrews, Galway, 1993

- Mathematics
- 1995

1. An army of cohomology against residual finiteness 2. On some questions concerning subnormally monomial groups 3. A conjecture concerning the evaluation of products of class-sums of the symmetric…

### Interval enforceable properties of finite groups

- Mathematics
- 2012

We propose a classification of group properties according to whether they can be deduced from the assumption that a group's subgroup lattice contains an interval isomorphic to some lattice. We are…

### Algebras, Lattices, Varieties

- Mathematics
- 1987

Introduction. Preliminaries. Basic concepts. Lattices. Unary and binary operations. Fundamental algebraic results. Unique factorization. Bibliography. Table of notation. Index.