共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we show that, given a complete lattice
, the following three
lattices are the same: (1) the lattice of closure relations on
, (2) the lattice of meet-closed subsets of
, and (3) the lattice of complete join congruence relations on
. 相似文献
2.
Cancellative residuated lattices are natural generalizations of lattice-ordered
groups (
-groups).
Although cancellative monoids are defined by quasi-equations, the class
of cancellative residuated lattices is a variety.
We prove that there are only two
commutative subvarieties of
that cover the trivial variety, namely the varieties
generated by the integers and the negative integers (with zero). We also construct examples
showing that in contrast to
-groups, the lattice reducts of cancellative residuated lattices
need not be distributive. In fact we prove that every lattice can be embedded in the
lattice reduct of a cancellative residuated lattice. Moreover, we show that there exists an
order-preserving injection of the lattice of all lattice varieties into the subvariety lattice of
.We define generalized MV-algebras and generalized BL-algebras and prove that the
cancellative integral members of these varieties are precisely the negative cones of
-groups, hence the latter form a variety, denoted by
. Furthermore we prove that the map that sends a subvariety of
-groups to the corresponding class of negative cones is a lattice
isomorphism from the lattice of subvarieties of
to the lattice of subvarieties of
.
Finally, we show how to translate equational bases between corresponding subvarieties, and
briefly discuss these results in the context of R. McKenzies characterization of categorically
equivalent varieties. 相似文献
3.
The probability that m randomly chosen elements
of a finite power associative loop
have prescribed orders and generate
is calculated in terms of certain constants
related to the action of Aut(
) on the subloop lattice of
. As an illustration, all meaningful
probabilities of random generation by elements of given orders are found for the smallest
nonassociative simple Moufang loop. 相似文献
4.
Hasse constants and their basic properties are introduced to facilitate the connection
between the lattice of subalgebras of an algebra
and the natural action of the automorphism group Aut(
) on
. These constants are then used to describe the lattice
of subloops of the smallest nonassociative simple Moufang loop. 相似文献
5.
We compare the two recently introduced semidirect product operations
*r and
*rr within the lattice of e-varieties of locally inverse
semigroups. For each e-variety
which
contains all rectangular bands and is properly contained in the e-variety of all completely
simple semigroups, the inclusions
are proved where
is the e-variety of all semilattices and
the variety of all abelian
groups of exponent dividing q where q is any
integer greater than one. Some consequences for the class of finite locally inverse semigroups are also obtained. 相似文献
6.
It is shown that an algebraic frame L is regular if
and only if its compact
elements are complemented. More generally, it is shown that each pseudocomplemented
element is regular if and only if each
, with c compact, is complemented.
With a mild assumption on L, each
, with c compact, is regular precisely
when
for any
two minimal primes p and q
of L. These results are then interpreted in various frames of
subobjects of lattice-ordered groups and f-rings. 相似文献
8.
To every egglike inversive plane
there is associated a family
of involutions of the point set of
such that
circles of
are the fixed point sets of the involutions in
. Korchmaros and Olanda characterized a family
of involutions on a set of size n2 + 1to be
for
an egglike inversive plane of order n by four conditions. In this
paper, we give an alternative proof where the Galois space PG(3,n) in
which
is embedded is built up directly by using concepts and
results on finite linear spaces. 相似文献
9.
In this note we show that the equational theory of all lattices is defined by the
single absorption law
This identity of length 29 with 8 variables is shorter than previously known such equations
defining lattices. 相似文献
11.
Let S be a real interval with
, and
be a function satisfying
We show that if h is Lebesgue or Baire measurable, then there
exists
such that
That result is motivated by a question of E. Manstaviius.
Received: 11 February 2003 相似文献
12.
Mark Pankov 《Journal of Geometry》2004,79(1-2):169-176
Let
be a finite-dimensional projective space
and
be the Grassmannian consisting of
all k-dimensional subspaces of
. In the paper we show that
transformations of
sending base subsets
to base subsets are induced by collineations of
to itself or to the dual projective space
.
This statement generalizes the main result of the authors paper [19]. 相似文献
13.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
14.
Summary.
In this paper we determine all iseomorphic pairs (isomorphic
pairs with monotonic, thus continuous isomorphisms) of
continuous, strictly increasing, linearly homogeneous functions defined on
cartesian squares
I
2 and
J
2 of
intervals of positive numbers or on their restrictions
or
and
or
We prove that, if the iseomorphy is nontrivial, then each
homogeneous function is a (weighted) geometric or power mean or a
joint pair of such means.
In functional equations terminology this means that all nontrivial
continuous strictly increasing linearly homogeneous solutions
G, H
(with the continuous strictly monotonic
F also unknown) of the
equation
on D
< or
D
>
are weighted geometric or power means, while on
I
2
they are joint pairs of weighted geometric means or of weighted
power means. 相似文献
15.
Let G be a connected simply connected almost
-simple algebraic group with
non-compact and
a cocompact congruence subgroup. For any homogeneous manifold
of finite volume, and a
, we show that the Hecke orbit T
a
(x
0
H) is equidistributed on
as
, provided H is a non-compact commutative reductive subgroup of G. As a corollary, we generalize the equidistribution result of Hecke points ([COU], [EO1]) to homogeneous spaces G/H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic
polynomial.
The second author partially supported by DMS 0333397.
Received: May 2005 Revision: March 2006 Accepted: June 2006 相似文献
16.
We prove that any variety
in which every factor congruence is compact has
Boolean factor congruences, i.e., for all A in
the set of factor congruences of A is a distributive sublattice of the congruence lattice
of A. 相似文献
17.
18.
We prove that a finite group G is
-constrained if and only if it contains a nilpotent subgroup
I satisfying
for all
.Received: 22 July 2002 相似文献
19.
Yun S. Song 《Annals of Combinatorics》2003,7(3):365-379
We study subtree-prune-and-regraft (SPR) operations on
leaf-labelled rooted binary trees, also known as rooted binary phylogenetic trees.
This study is motivated by the problem of
graphically representing evolutionary histories of biological sequences subject to recombination.
We investigate some basic properties of the induced SPR-metric on the space
of leaf-labelled
rooted binary trees with n leaves. In contrast to the case of
unrooted trees, the number |U(T)| of trees in
which are one SPR operation away from a given tree
depends on the
topology of T. In this paper, we construct recursion relations which allow one to determine the
unit-neighbourhood size |U(T)| efficiently for any tree topology. In fact, using the recursion
relations we are able to derive a simple closed-form formula for the unit-neighbourhood size.
As a corollary, we construct sharp upper and lower bounds on the size of unit-neighbourhoods
and investigate the diameter of
.
Lastly, we consider an enumeration problem relevant to population genetics.AMS Subject Classification: 05C05, 92D15. 相似文献
20.
Proof of the Ergodic Hypothesis
for Typical Hard Ball Systems 总被引:3,自引:0,他引:3
We consider the system of
hard balls with masses
and radius r in the flat torus
of size
. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost
every selection
of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the
case
. The method of that proof was primarily dynamical-geometric, whereas
the present approach is inherently algebraic.
Communicated by Eduard ZehnderSubmitted 17/10/02, accepted 01/12/03 相似文献