On the subalgebra lattice of Peano algebras with finitary and infinitary operations

1995 ◽  
Vol 33 (2) ◽  
pp. 169-185
Author(s):  
K. -H. Diener
Keyword(s):  
Subalgebra Lattice

The subalgebra lattice of a Heyting algebra

1987 ◽  
Vol 37 (1) ◽  
pp. 34-41 ◽  
Author(s):  
L. Vrancken-Mawet ◽  
Georges Hansoul
Keyword(s):  
Heyting Algebra ◽  
Subalgebra Lattice

scholarly journals ON SEMI-MODULAR SUBALGEBRAS OF LIE ALGEBRAS OVER FIELDS OF ARBITRARY CHARACTERISTIC

2008 ◽  
Vol 01 (02) ◽  
pp. 283-294 ◽  
Author(s):  
DAVID A. TOWERS
Keyword(s):  
Lie Algebras ◽  
Extensive Study ◽  
Two Dimensional ◽  
Perfect Field ◽  
Characteristic P ◽  
Subalgebra Lattice ◽  
Closed Fields ◽  
The One ◽  
Algebraically Closed Fields ◽  
Number Of Authors

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over algebraically closed fields of characteristic p > 0 that have absolute toral rank ≤ 1 or are restricted, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a perfect field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3.

scholarly journals Lower semimodular Lie algebras

1999 ◽  
Vol 42 (3) ◽  
pp. 521-540 ◽  
Author(s):  
V. R. Varea
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Subalgebras ◽  
Modular Element ◽  
Subalgebra Lattice ◽  
The Relationship

This paper is concerned with the relationship between the properties of the subalgebra lattice ℒ(L) of a Lie algebra L and the structure of L. If the lattice ℒ(L) is lower semimodular, then the Lie algebra L is said to be lower semimodular. If a subalgebra S of L is a modular element in the lattice ℒ(L), then S is called a modular subalgebra of L. The easiest condition to ensure that L is lower semimodular is that dim A/B = 1 whenever B < A ≤ L and B is maximal in A (Lie algebras satisfying this condition are called sχ-algebras). Our aim is to characterize lower semimodular Lie algebras and sχ-algebras, over any field of characteristic greater than three. Also, we obtain results about the influence of two solvable modularmaximal subalgebras on the structure of the Lie algebra and some results on the structure of Lie algebras all of whose maximal subalgebras are modular.

scholarly journals On the subalgebra lattice of a Leibniz algebra

2021 ◽  
pp. 1-13
Author(s):  
Salvatore Siciliano ◽  
David A. Towers
Keyword(s):  
Leibniz Algebra ◽  
Subalgebra Lattice

A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE

2013 ◽  
Vol 23 (01) ◽  
pp. 1-35
Author(s):  
KONRAD PIÓRO
Keyword(s):  
Finite Type ◽  
Locally Finite ◽  
Finite Algebras ◽  
Edge Disjoint ◽  
Subalgebra Lattice ◽  
Strong Property ◽  
Directed Hypergraphs ◽  
Algebraic Result ◽  
Directed Hypergraph

The aim of this paper is to show that the weak subalgebra lattice uniquely determines the subalgebra lattice for locally finite algebras of a fixed finite type. However, this algebraic result turns out to be a very particular case of the following hypergraph result (which is interesting itself): A total directed hypergraph D of finite type is uniquely determined, in the class of all the directed hypergraphs of this type, by its skeleton up to the orientation of some pairwise edge-disjoint directed hypercycles and hyperpaths. The skeleton of D is a hypergraph obtained from D by omitting the orientation of all edges.

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