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Page 672 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

See also 05011, 05051, 05088, 13029, 16045, 20064, 52004, 52015.
06B

*Lattices*95b:06011 06B05 68P05 Buckle, John (4-WARW-C; Coventry)*A**characterisation**of**meet**and**join**respecting**pre*-*orders**and**congruences*...*congruences**and**pre*-*orders**on*computers.” ...##
###
Congruence frames of frames and κ-frames
[article]

2022
*
arXiv
*
pre-print

We describe the

arXiv:2201.08897v1
fatcat:aqozna2xrbef3ifphd2a4o5ply
*congruence**lattices**of*frames*and*κ-frames. ... We look at the role that*congruence*biframes play in the category*of*strictly zero-dimensional biframes*and*discuss some reflections*and*coreflections*of**congruence*frames. ... Frith*and*Professor C.R.A. Gilmour for their help, encouragement*and*patience. I am grateful for the freedom to pursue*a*topic that I found interesting. ...##
###
Page 1313 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

*A*principal

*congruence*

*on*

*a*double demi-p-

*lattice*is expressed as

*a*

*join*

*of*countably many principal

*lattice*

*congruences*. ... 1313 elements contained in the

*join*

*of*

*finitely*many others is contained in

*one*

*of*them. ...

##
###
Functions and equations in classes of distributive lattices with pseudocomplementation

1974
*
Proceedings of the Edinburgh Mathematical Society
*

*Of*course, any

*congruence*

*on*S(L), regarded as

*a*member

*of*38

*a*, is

*a*

*congruence*

*on*S(L) regarded as

*a*member

*of*3S 0

*and*visa versa. ... u $&

*a*, 38 x ,ye,

*and*38 0

*respectively*. ...

*of*distributive

*lattices*with 0

*and*1 (

*and*0, 1-preserving

*lattice*homomorphisms)

*and*call it the

*pre*-Post algebra

*of*

*order*n over D. ...

##
###
The Lattice of One-Sided Congruences on an Inverse Semigroup
[article]

2019
*
arXiv
*
pre-print

It is shown that that every

arXiv:1901.11455v1
fatcat:e6roeyxhj5dtdlciz3wk2c2otq
*finitely*generated left*congruence*is the*join**of**a**finitely*generated trace minimal left*congruence**and**a**finitely*generated idempotent separating left*congruence*. ... The*lattice**of*left*congruences*is identified as*a*subset*of*the direct product*of*the*lattice**of**congruences**on*the idempotents*and*the*lattice**of*full inverse subsemigroups. ... Acknowledgements This project forms part*of*the work toward my PhD at the University*of*York, funded by EPSRC. ...##
###
Monotone clones, residual smallness and congruence distributivity

1990
*
Bulletin of the Australian Mathematical Society
*

We produce several

doi:10.1017/s0004972700018104
fatcat:vqu5f3yjaffxtdradmlstj6hb4
*characterisations**of*the*finite*bounded*ordered*sets for which the corresponding variety is*congruence*-distributive. ... Corresponding to each*ordered*set there is*a*variety, determined up to equivalence, generated by an algebra whose term operations are all the monotone operations*on*the*ordered*set. ... to {c, d} , these polynomials become the*join**and**meet**of**a*two-element*lattice*. ...##
###
Residuated Structures and Orthomodular Lattices

2021
*
Studia Logica: An International Journal for Symbolic Logic
*

Among the outliers,

doi:10.1007/s11225-021-09946-1
fatcat:dxrdrsqzrvdernu4szolos4u4i
*one*counts orthomodular*lattices**and*other varieties*of*quantum algebras. ... We investigate the*lattice**of*subvarieties*of*pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals,*and*develop*a*theory*of*left nuclei. ... Paoli acknowledges the support*of*MIUR within the project PRIN 2017: "Theory*and*applications*of*resource sensitive logics", CUP: 20173WKCM5. D. Fazio*and**A*. ...##
###
Duality and Recognition
[chapter]

2011
*
Lecture Notes in Computer Science
*

The fact that

doi:10.1007/978-3-642-22993-0_3
fatcat:wypwkdeib5gvxaibobuobdlhui
*one*can associate*a**finite*monoid with universal properties to each language recognised by an automaton is central to the solution*of*many practical*and*theoretical problems in automata theory ... In the case*of**a**finite*distributive*lattice*, filters*and*ideals are all principal generated by their*meet**and*their*join*,*respectively*. ... Also, Con ω (*A*) is*ordered*by reverse set inclusion*and*is directed in this*order*since the intersection*of*two*congruences**of**finite*index is again*a**congruence**of**finite*index. ...##
###
Equality algebras

1997
*
Bulletin of the Australian Mathematical Society
*

In such

doi:10.1017/s0004972700030902
fatcat:6fnzb4u73ndulj5pqtsfpp4szu
*a*case E constitutes*a*complete*lattice*in which*meet*is intersection, the*join*p x V p 2 is the intersection*of*all*congruences*in E containing both p\*and*P2,*and*the bottom element is 0 = f| ...*LATTICE**OF**CONGRUENCES**CHARACTERISATION*There is*a**characterisation*following Proposition 2.3 also. THEOREM 4 . 6 . The internalised equality = t*on**A*is equivalent to o c , where C = C =i . ... ; then E is*a*subsemilattice*of*C, closed under ideal sums (that is, ideal*meets*with*respect*to the partial*order**of*interest here),*and*moreover [O\E = [*a*]c is the ideal generated by*a*-b, so the ring ...##
###
On E-pseudovarieties of finite regular semigroups

2008
*
Bulletin of the Australian Mathematical Society
*

In particular, great thanks go to my supervisor Graham Clarke, who first introduced me to the delights

doi:10.1017/s0004972708000294
fatcat:jo4rwxy7a5gwrcak2646rbngdy
*of*algebraic semigroup theory*and*suggested the initial direction*of*research. ... My second supervisor Kathy Horadam was always encouraging*and*ready to give great advice. ...*A**lattice*L is said to be*a*complete*lattice*if every nonempty subset*A**of*L has*a**meet**a*∈*A**a**and**a**join**a*∈*A**a*. The following result is well known. ...##
###
Models of Relevant Arithmetic

2022
*
The Australasian Journal of Logic
*

In this paper we consider the DeMorgan monoids in which R# can be modelled, deriving

doi:10.26686/ajl.v19i1.6585
fatcat:akx2fj3cujey5fbx7qeukiwk3a
*a*fairly complete account*of*those modelling the stronger arithmetic RM# modulo n*and**a*partial account for the case ...*of*R# modulo*a*prime number. ... The tables for conjunction*and*disjunction (*lattice**meet**and**join*) can be read off the Hasse diagram in the usual way. ...##
###
Congruences on infinite partition and partial Brauer monoids
[article]

2021
*
arXiv
*
pre-print

As

arXiv:1809.07427v2
fatcat:fx7vnsvkgrao5nk2fxenjxzpmq
*a*consequence*of*our classification result, we show that the*congruence**lattices**of*P_X*and*PB_X are isomorphic to each other,*and*are distributive*and*well quasi-*ordered*. ... We give*a*complete description*of*the*congruences**on*the partition monoid P_X*and*the partial Brauer monoid PB_X, where X is an arbitrary infinite set,*and*also*of*the*lattices*formed by all such*congruences*... We also thank the referee for their careful reading*of*the paper,*and*for their valuable suggestions, especially for pointing out the second clause in Corollary 8.2. ...##
###
Topological duality for distributive lattices, and applications
[article]

2022
*
arXiv
*
pre-print

This preprint version contains the first part

arXiv:2203.03286v2
fatcat:bs6pfodmkfgnhpegiuvcymb3fy
*of*the book,*a*graduate level 'crash course' in duality theory as it is practiced now,*and**a*chapter*on*applications to domain theory. ... Our aim is to get in*a*fairly full palette*of*duality tools as directly*and*quickly as possible, then to illustrate*and*further elaborate these tools within the setting*of*three emblematic applications ... As we saw in Section 1.3, in*a**finite*distributive*lattice*, each element is*a**finite**join**of**join*irreducible elements*and**a**finite**meet**of**meet*irreducible elements. ...##
###
Abstraction, Up-To Techniques and Games for Systems of Fixpoint Equations

2020
*
International Conference on Concurrency Theory
*

Additionally, relying

doi:10.4230/lipics.concur.2020.25
dblp:conf/concur/Baldan0P20
fatcat:ntk5jqiye5buxfc6gs22phblny
*on*the approximation theory, we can*characterise*the solution*of*systems*of*fixpoint equations over complete*lattices*in terms*of**a*suitable parity game, generalising some recent ... Systems*of*fixpoint equations over complete*lattices*, consisting*of*(mixed) least*and*greatest fixpoint equations, allow*one*to express many verification tasks such as model-checking*of*various kinds*of*... The*join**and*the*meet**of**a*subset X ⊆ P (if they exist) are denoted X*and*X,*respectively*. Definition 1 (complete*lattice*, basis). ...##
###
2. Abstracts Invited Speakers

2013
*
Journal of Perinatal Medicine
*

As

doi:10.1515/jpm-2013-2001
fatcat:uzvmvs2t7rcbznk3yhwaaobvly
*a*byproduct*of*our study we describe the*meets**of*extremal states*on*MV-algebras*and*we give*a*new characterization*of*extremal states. ...*A*natural*lattice**order**on*M n (R) to make it into*a**lattice*-*ordered*ring is the entrywise*lattice**order*in which*a*matrix*A*= (*a*ij ) ∈ M n (R) is positive if each*a*ij is positive in R. ...
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