Results 221 to 230 of about 165,943,886 (264)

Varieties of Orthomodular Lattices

open access: yesCanadian Journal of Mathematics, 1971
In this paper we start investigating the lattice of varieties of orthomodular lattices. The varieties studied here are those generated by orthomodular lattices which are the horizontal sum of Boolean algebras. It turns out that these form a principal ideal in the lattice of all varieties of orthomodular lattices.
Bruns, Günter, Kalmbach, Gudrun
core   +3 more sources

Varieties of lattices [PDF]

open access: yes, 1988
An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of information has been obtained in the last twenty years.
Jipsen, Peter
core   +3 more sources

Primitive lattice varieties

International Journal of Algebra and Computation, 2022
A variety is primitive if every subquasivariety is equational, i.e. a subvariety. In this paper, we explore the connection between primitive lattice varieties and Whitman’s condition (W). For example, if every finite subdirectly irreducible lattice in a locally finite variety [Formula: see text] satisfies Whitman’s condition (W), then [Formula: see ...
Peter Jipsen, James B. Nation
openaire   +3 more sources

On the variety of strong subresiduated lattices

Mathematical Logic Quarterly, 2023
AbstractA subresiduated lattice is a pair , whereAis a bounded distributive lattice,Dis a bounded sublattice ofAand for every there exists the maximum of the set , which is denoted by . This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where . The class of subresiduated lattices is a variety which properly contains the variety of Heyting
Sergio A. Celani   +1 more
openaire   +4 more sources

LATTICES OF VARIETIES OF ALGEBRAS

Mathematics of the USSR-Sbornik, 1980
Let be an associative and commutative ring with 1, a subsemigroup of the multiplicative semigroup of , not containing divisors of zero, and some variety of -algebras. A study is made of the homomorphism from the lattice of all subvarieties of into the lattice of all varieties of -algebras, which is induced in a certain natural sense by the ...
openaire   +3 more sources

Varieties of Demi‐Pseudocomplemented Lattices

Mathematical Logic Quarterly, 1991
The authors present a solution to the problem of desribing the structure of the lattice of subvarieties of the variety of demi \(p\)-lattices, and in particular of almost \(p\)-lattices. The main purpose is to present an infinite poset \(P_ 0\) whose Hasse diagram is completely described by the following property: The lattice of subvarieties of the ...
openaire   +3 more sources

Splittings in the variety of residuated lattices

Algebra Universalis, 2000
A pair \(( {\mathcal V}_1, {\mathcal V}_2)\) of subvarieties of a variety \(\mathcal V\) is called a splitting pair if \({\mathcal V}_1 \not \subseteq {\mathcal V}_2\) and for any subvariety \(\mathcal S\) of \(\mathcal V\) either \({\mathcal V}_1 \subseteq \mathcal S\) or \({\mathcal S} \subseteq {\mathcal V}_2\). In such a case, \({\mathcal V}_1\) is
Kowalski, Tomasz, Ono, Hiroakira
openaire   +3 more sources

A Subsemilattice of the Lattice of Varieties of Lattice Ordered Groups

Canadian Journal of Mathematics, 1981
Each variety of lattice ordered groups determines a variety of groups, namely the variety of groups generated by the groups i n . In this paper a completely new and different correspondence between varieties of groups and varieties of lattice ordered groups is developed.
openaire   +1 more source

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