On Finitely Generated Lattices of Finite Width

1981 ◽  
Vol 33 (1) ◽  
pp. 28-48 ◽  
Author(s):  
W. Poguntke ◽  
B. Sands
Keyword(s):  
Finite Width ◽  
Subdirectly Irreducible ◽  
Finitely Generated ◽  
Simple Lattice ◽  
Irreducible Lattice ◽  
Made In

The width of a lattice L is the maximum number of pairwise noncomparable elements in L.It has been known for some time ([5] ; see also [4]) that there is just one subdirectly irreducible lattice of width twro, namely the five-element nonmodular lattice N5. It follows that every lattice of width two is in the variety of N5, and that every finitely generated lattice of width two is finite.Beginning a study of lattices of width three, W. Poguntke [6] showed that there are infinitely many finite simple lattices of width three. Further studies on width three lattices were made in [3], where it was asked whether every finitely generated simple lattice of width three is finite. In this paper we will show that, in fact, more is true:THEOREM 1.1. Every finitely generated subdirectly irreducible lattice of width three is finite.

Congruence Normal Covers of Finitely Generated Lattice Varieties

1992 ◽  
Vol 35 (3) ◽  
pp. 311-320 ◽  
Author(s):  
Alan Day ◽  
J. B. Nation
Keyword(s):  
Convex Sets ◽  
Finite Lattice ◽  
Subdirectly Irreducible ◽  
Finitely Generated ◽  
Irreducible Lattice

AbstractWe consider certain pseudovarieties K of lattices which are closed under the doubling of convex sets. For each such K, given an arbitrary finite lattice 𝓛, we describe the covers of the variety V(𝓛) of the form V(𝓛, K) with K a subdirectly irreducible lattice in K.

scholarly journals Rings whose additive endomorphisms are ring endomorphisms

1990 ◽  
Vol 42 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Gary Birkenmeier ◽  
Henry Heatherly
Keyword(s):  
Subdirectly Irreducible ◽  
Finiteness Conditions ◽  
Chain Conditions ◽  
Open Questions ◽  
Open Case ◽  
Ring Endomorphism ◽  
Substantial Progress ◽  
Additive Endomorphism ◽  
Made In

A ring R is said to be an AE-ring if every additive endomorphism is a ring endomorphism. In this paper further steps are made toward solving Sullivan's Problem of characterising these rings. The classification of AE-rings with. R3 ≠ 0 is completed. Complete characterisations are given for AE-rings which are either: (i) subdirectly irreducible, (ii) algebras over fields, or (iii) additively indecomposable. Substantial progress is made in classifying AE-rings which are mixed – the last open case – by imposing various finiteness conditions (chain conditions on special ideals, height restricting conditions). Several open questions are posed.

scholarly journals VARIETIES OF DE MORGAN MONOIDS: COVERS OF ATOMS

2019 ◽  
Vol 13 (2) ◽  
pp. 338-374 ◽  
Author(s):  
T. MORASCHINI ◽  
J. G. RAFTERY ◽  
J. J. WANNENBURG
Keyword(s):  
The Other ◽  
Subdirectly Irreducible ◽  
Finitely Generated ◽  
Irreducible Algebra ◽  
Subdirectly Irreducible Algebra ◽  
Discriminator Varieties ◽  
Subvariety Lattice ◽  
Image Position

AbstractThe variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM (together with the trivial De Morgan monoids) constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety (C4) within U are revealed here. There are just ten of them (all finitely generated). In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of (C4) [or of (D4)] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids.

Heat Transfer During Wind Flow over Rectangular Bodies in the Natural Environment

1981 ◽  
Vol 103 (2) ◽  
pp. 262-267 ◽  
Author(s):  
F. L. Test ◽  
R. C. Lessmann ◽  
A. Johary
Keyword(s):  
Heat Transfer ◽  
Experimental Investigation ◽  
Wind Flow ◽  
Finite Width ◽  
Two Dimensional ◽  
Disturbance Intensity ◽  
Temperature Heat ◽  
Two Dimensional Flow ◽  
Transfer Behavior ◽  
Made In

An experimental investigation has been performed to determine the constant temperature heat transfer behavior on the upper surface of a rectangular plate with a chord length of 122 cm (48 in.), a width of 81.3 cm (32 in.) and a thickness aspect ratio of 6/1. Special side attachments were made in order to maintain approximately two-dimensional flow over the finite width body when exposed to varying wind directions. The angle of attack was 40 deg or greater. Quasi-local values of STRe were found to be 200 percent higher than wind tunnel values and 300 percent higher than analytical predictions. The disturbance intensity of the wind flow was in the range of 20 to 50 percent and is thought to be related to the increase in heat transfer since the flow over the plate was found to be laminar.

scholarly journals Optimal natural dualities: the role of endomorphisms

2004 ◽  
Vol 77 (2) ◽  
pp. 269-296
Author(s):  
M. J. Saramago
Keyword(s):  
Finite Algebra ◽  
Subdirectly Irreducible ◽  
Minimal Elements ◽  
Irreducible Lattice ◽  
The Way

AbstractThe optimality of dualities on a quasivariety , generated by a finite algebra , has been introduced by Davey and Priestley in the 1990s. Since every optimal duality is determined by a transversal of a certain family of subsets of Ω, where Ω is a given set of relations yielding a duality on , an understanding of the structures of these subsets—known as globally minimal failsets—was required. A complete description of globally minimal failsets which do not contain partial endomorphisms has recently been given by the author and H. A. Priestley. Here we are concerned with globally minimal failsets containing endomorphisms. We aim to explain what seems to be a pattern in the way endomorphisms belong to these failsets. This paper also gives a complete description of globally minimal failsets whose minimal elements are automorphisms, when is a subdirectly irreducible lattice-structured algebra.

scholarly journals Trees as commutative BCK-Algebras

1981 ◽  
Vol 23 (2) ◽  
pp. 181-190
Author(s):  
William H. Cornish
Keyword(s):  
Height Function ◽  
Chain Condition ◽  
New Method ◽  
Subdirectly Irreducible ◽  
Natural Numbers ◽  
Finitely Generated ◽  
Congruence Distributivity ◽  
Finite Height ◽  
Descending Chain Condition ◽  
Simple Algebras

A new method of constructing commutative BCK-algebras is given. It depends upon the notion of a valuation of a lower semilattice in a given commutative BCK-algebra. Any tree vith the descending chain condition has a valuation in the natural numbers, considered as a commutative BCK-algebra; the valuation is the height-function. Thus, any tree of finite height possesses a uniquely determined commutative BCK-structure. The finite trees with at most one atom and height at most n are precisely the finitely generated subdirectly irreducible (simple) algebras in the subvariety of commutative BCK-algebras which satisfy the identity (En): xyn = xyn+1. Due to congruence-distributivity, it is then possible to describe the associated lattice of subvarieties.

Iterative separation in distributive congruence lattices

2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Miroslav Ploščica
Keyword(s):  
Close Connection ◽  
Subdirectly Irreducible ◽  
Finitely Generated ◽  
Distributive Variety ◽  
Algebraic Lattices ◽  
Congruence Lattices ◽  
Congruence Distributive Variety ◽  
Congruence Distributive ◽  
Subdirectly Irreducible Algebras

AbstractIn [PLOŠČICA, M.: Separation in distributive congruence lattices, Algebra Universalis 49 (2003), 1–12] we defined separable sets in algebraic lattices and showed a close connection between the types of non-separable sets in congruence lattices of algebras in a finitely generated congruence distributive variety and the structure of subdirectly irreducible algebras in . Now we generalize these results using the concept of separable mappings (defined on some trees) and apply them to some lattice varieties.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Surface Structure in Microtomed Sections Caused by Glass and Diamond Knives

1971 ◽  
Vol 29 ◽  
pp. 456-457
Author(s):  
J. Temple Black ◽  
William G. Boldosser
Keyword(s):  
Plastic Deformation ◽  
Epoxy Resin ◽  
Carbon Coating ◽  
Surface Damage ◽  
Body Angle ◽  
Normal Manner ◽  
Bottom Side ◽  
Cutting Direction ◽  
Made In ◽  
Diamond Knife

Ultramicrotomy produces plastic deformation in the surfaces of microtomed TEM specimens which can not generally be observed unless special preparations are made. In this study, a typical biological composite of tissue (infundibular thoracic attachment) infiltrated in the normal manner with an embedding epoxy resin (Epon 812 in a 60/40 mixture) was microtomed with glass and diamond knives, both with 45 degree body angle. Sectioning was done in Portor Blum Mt-2 and Mt-1 microtomes. Sections were collected on formvar coated grids so that both the top side and the bottom side of the sections could be examined. Sections were then placed in a vacuum evaporator and self-shadowed with carbon. Some were chromium shadowed at a 30 degree angle. The sections were then examined in a Phillips 300 TEM at 60kv.Carbon coating (C) or carbon coating with chrom shadowing (C-Ch) makes in effect, single stage replicas of the surfaces of the sections and thus allows the damage in the surfaces to be observable in the TEM. Figure 1 (see key to figures) shows the bottom side of a diamond knife section, carbon self-shadowed and chrom shadowed perpendicular to the cutting direction. Very fine knife marks and surface damage can be observed.

Iron storage sites in the myocardium as revealed by cytohistochemistry

1988 ◽  
Vol 46 ◽  
pp. 394-395
Author(s):  
M. Ashraf ◽  
F. Thompson ◽  
S. Miki ◽  
P. Srivastava
Keyword(s):  
Cardiac Tissue ◽  
Coronary Perfusion ◽  
Intracellular Iron ◽  
Ether Anesthesia ◽  
Intense Staining ◽  
Iron Storage ◽  
Thin Sections ◽  
Rat Hearts ◽  
Cacodylate Buffer ◽  
Made In

Iron is believed to play an important role in the pathogenesis of ischemic injury. However, the sources of intracellular iron in myocytes are not yet defined. In this study we have attempted to localize iron at various cellular sites of the cardiac tissue with the ferrocyanide technique.Rat hearts were excised under ether anesthesia. They were fixed with coronary perfusion with 3% buffered glutaraldehyde made in 0.1 M cacodylate buffer pH 7.3. Sections, 60 μm in thickness, were cut on a vibratome and were incubated in the medium containing 500 mg of potassium ferrocyanide in 49.5 ml H2O and 0.5 ml concentrated HC1 for 30 minutes at room temperature. Following rinses in the buffer, tissues were dehydrated in ethanol and embedded in Spurr medium.The examination of thin sections revealed intense staining or reaction product in peroxisomes (Fig. 1).

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