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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]

Graham Manuell
2022 arXiv   pre-print
We describe the 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.  ... 
arXiv:2201.08897v1 fatcat:aqozna2xrbef3ifphd2a4o5ply

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

R. Beazer
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.  ... 
doi:10.1017/s0013091500010312 fatcat:xtbl5qukwbcefopg27i36o7lae

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

Matthew Brookes
2019 arXiv   pre-print
It is shown that that every 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.  ... 
arXiv:1901.11455v1 fatcat:e6roeyxhj5dtdlciz3wk2c2otq

Monotone clones, residual smallness and congruence distributivity

Ralph McKenzie
1990 Bulletin of the Australian Mathematical Society  
We produce several 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.  ... 
doi:10.1017/s0004972700018104 fatcat:vqu5f3yjaffxtdradmlstj6hb4

Residuated Structures and Orthomodular Lattices

D. Fazio, A. Ledda, F. Paoli
2021 Studia Logica: An International Journal for Symbolic Logic  
Among the outliers, 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.  ... 
doi:10.1007/s11225-021-09946-1 fatcat:dxrdrsqzrvdernu4szolos4u4i

Duality and Recognition [chapter]

Mai Gehrke
2011 Lecture Notes in Computer Science  
The fact that 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.  ... 
doi:10.1007/978-3-642-22993-0_3 fatcat:wypwkdeib5gvxaibobuobdlhui

Equality algebras

Desmond Fearnley-Sander, Tim Stokes
1997 Bulletin of the Australian Mathematical Society  
In such 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  ... 
doi:10.1017/s0004972700030902 fatcat:6fnzb4u73ndulj5pqtsfpp4szu

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 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 aA a and a join aA a. The following result is well known.  ... 
doi:10.1017/s0004972708000294 fatcat:jo4rwxy7a5gwrcak2646rbngdy

Models of Relevant Arithmetic

John Slaney
2022 The Australasian Journal of Logic  
In this paper we consider the DeMorgan monoids in which R# can be modelled, deriving 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.  ... 
doi:10.26686/ajl.v19i1.6585 fatcat:akx2fj3cujey5fbx7qeukiwk3a

Congruences on infinite partition and partial Brauer monoids [article]

James East, Nik Ruskuc
2021 arXiv   pre-print
As 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.  ... 
arXiv:1809.07427v2 fatcat:fx7vnsvkgrao5nk2fxenjxzpmq

Topological duality for distributive lattices, and applications [article]

Mai Gehrke, Sam van Gool
2022 arXiv   pre-print
This preprint version contains the first part 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.  ... 
arXiv:2203.03286v2 fatcat:bs6pfodmkfgnhpegiuvcymb3fy

Abstraction, Up-To Techniques and Games for Systems of Fixpoint Equations

Paolo Baldan, Barbara König, Tommaso Padoan, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Additionally, relying 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).  ... 
doi:10.4230/lipics.concur.2020.25 dblp:conf/concur/Baldan0P20 fatcat:ntk5jqiye5buxfc6gs22phblny

2. Abstracts Invited Speakers

2013 Journal of Perinatal Medicine  
As 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.  ... 
doi:10.1515/jpm-2013-2001 fatcat:uzvmvs2t7rcbznk3yhwaaobvly
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