Cycle-finite algebras with almost all indecomposable modules of projective or injective dimension at most one

2013 ◽  
Vol 132 (2) ◽  
pp. 239-270 ◽  
Author(s):  
Adam Skowyrski
Keyword(s):  
Injective Dimension ◽  
Indecomposable Modules ◽  
Finite Algebras ◽  
Almost All

scholarly journals Complete slices and homological properties of tilted algebras

1994 ◽  
Vol 36 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Ibrahim Assem ◽  
Flávio Ulhoa Coelho
Keyword(s):  
Representation Theory ◽  
Global Dimension ◽  
Indecomposable Modules ◽  
Tilted Algebra ◽  
Finite Dimensional ◽  
Tilted Algebras ◽  
Homological Dimensions ◽  
The Subject ◽  
Left And Right ◽  
Almost All

It is reasonable to expect that the representation theory of an algebra (finite dimensional over a field, basic and connected) can be used to study its homological properties. In particular, much is known about the structure of the Auslander-Reiten quiver of an algebra, which records most of the information we have on its module category. We ask whether one can predict the homological dimensions of a module from its position in the Auslander-Reiten quiver. We are particularly interested in the case where the algebra is a tilted algebra. This class of algebras of global dimension two, introduced by Happel and Ringel in [7], has since then been the subject of many investigations, and its representation theory is well understood by now (see, for instance, [1], [7], [8], [9], [11], [13]).In this case, the most striking feature of the Auslander-Reiten quiver is the existence of complete slices, which reproduce the quiver of the hereditary algebra from which the tilted algebra arises. It follows from well-known results that any indecomposable successor (or predecessor) of a complete slice has injective (or projective, respectively) dimension at most one, from which one deduces that a tilted algebra is representation-finite if and only if both the projective and the injective dimensions of almost all (that is, all but at most finitely many non-isomorphic) indecomposable modules equal two (see (3.1) and (3.2)). On the other hand, the authors have shown in [2, (3.4)] that a representation-infinite algebra is concealed if and only if both the projective and the injective dimensions of almost all indecomposable modules equal one (see also [14]). This leads us to consider, for tilted algebras which are not concealed, the case when the projective (or injective) dimension of almost all indecomposable successors (or predecessors, respectively) of a complete slice equal two. In order to answer this question, we define the notions of left and right type of a tilted algebra, then those of reduced left and right types (see (2.2) and (3.4) for the definitions).

scholarly journals Strongly simply connected Auslander algebras

1997 ◽  
Vol 39 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Ibrahim Assem ◽  
Peter Brown
Keyword(s):  
Representation Theory ◽  
Closed Field ◽  
Interesting Problem ◽  
Indecomposable Modules ◽  
Finite Algebras ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Infinite Case ◽  
Simple Connectedness ◽  
Simply Connected

Letkbe an algebraically closed field. By an algebra is meant an associative finite dimensionalk-algebra A with an identity. We are interested in studying the representation theory of Λ, that is, in describing the category mod Λ of finitely generated right Λ-modules. Thus we may, without loss of generality, assume that Λ is basic and connected. For our purpose, one strategy consists in using covering techniques to reduce the problem to the case where the algebra is simply connected, then in solving the problem in this latter case. This strategy was proved efficient for representation-finite algebras (that is, algebras having only finitely many isomorphism classes of indecomposable modules) and representation-finite simply connected algebras are by now well-understood: see, for instance [5], [7],[8]. While little is known about covering techniques in the representation-infinite case, it is clearly an interesting problem to describe the representation-infinite simply connected algebras. The objective of this paper is to give a criterion for the simple connectedness of a class of (mostly representationinfinite) algebras.

Cycle-Finite Algebras with Finitely Many τ-Rigid Indecomposable Modules

2016 ◽  
Vol 44 (5) ◽  
pp. 2048-2057 ◽  
Author(s):  
Piotr Malicki ◽  
Andrzej Skowroński
Keyword(s):  
Indecomposable Modules ◽  
Finite Algebras

Habitat Association of Klebsiella Species

1985 ◽  
Vol 6 (2) ◽  
pp. 52-58 ◽  
Author(s):  
Susan T. Bagley
Keyword(s):  
Drinking Water ◽  
Gastrointestinal Tract ◽  
Surface Waters ◽  
Industrial Effluents ◽  
Opportunistic Pathogen ◽  
Habitat Associations ◽  
Habitat Association ◽  
Klebsiella Species ◽  
Almost All ◽  
Polluted Waters

AbstractThe genus Klebsiella is seemingly ubiquitous in terms of its habitat associations. Klebsiella is a common opportunistic pathogen for humans and other animals, as well as being resident or transient flora (particularly in the gastrointestinal tract). Other habitats include sewage, drinking water, soils, surface waters, industrial effluents, and vegetation. Until recently, almost all these Klebsiella have been identified as one species, ie, K. pneumoniae. However, phenotypic and genotypic studies have shown that “K. pneumoniae” actually consists of at least four species, all with distinct characteristics and habitats. General habitat associations of Klebsiella species are as follows: K. pneumoniae—humans, animals, sewage, and polluted waters and soils; K. oxytoca—frequent association with most habitats; K. terrigena— unpolluted surface waters and soils, drinking water, and vegetation; K. planticola—sewage, polluted surface waters, soils, and vegetation; and K. ozaenae/K. rhinoscleromatis—infrequently detected (primarily with humans).

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

Electron microscopy studies of plasma-sprayed materials

1983 ◽  
Vol 41 ◽  
pp. 70-71
Author(s):  
K.R. Subramanian ◽  
A.H. King ◽  
H. Herman
Keyword(s):  
Plasma Spraying ◽  
Substrate Surface ◽  
Flame Temperature ◽  
Ceramic Coatings ◽  
Metallic Substrates ◽  
Hot Plasma ◽  
Almost All ◽  
Plasma Sprayed ◽  
Hostile Environments ◽  
Plasma Spraying Process

Plasma spraying is a technique which is used to apply coatings to metallic substrates for a variety of purposes, including hardfacing, corrosion resistance and thermal barrier applications. Almost all of the applications of this somewhat esoteric fabrication technique involve materials in hostile environments and the integrity of the coatings is of paramount importance: the effects of process variables on such properties as adhesive strength, cohesive strength and hardness of the substrate/coating system, however, are poorly understood.Briefly, the plasma spraying process involves forming a hot plasma jet with a maximum flame temperature of approximately 20,000K and a gas velocity of about 40m/s. Into this jet the coating material is injected, in powder form, so it is heated and projected at the substrate surface. Relatively thick metallic or ceramic coatings may be speedily built up using this technique.

Vacuum System to Minimize the Specimen Contamination of High-Performance EM

1977 ◽  
Vol 35 ◽  
pp. 68-69
Author(s):  
N. Yoshimura ◽  
K. Shirota ◽  
T. Etoh
Keyword(s):  
Electron Microscope ◽  
High Speed ◽  
High Performance ◽  
High Vacuum ◽  
Vacuum System ◽  
Pump System ◽  
Pumping System ◽  
Diffusion Pump ◽  
Almost All ◽  
Cascade Type

One of the most important requirements for a high-performance EM, especially an analytical EM using a fine beam probe, is to prevent specimen contamination by providing a clean high vacuum in the vicinity of the specimen. However, in almost all commercial EMs, the pressure in the vicinity of the specimen under observation is usually more than ten times higher than the pressure measured at the punping line. The EM column inevitably requires the use of greased Viton O-rings for fine movement, and specimens and films need to be exchanged frequently and several attachments may also be exchanged. For these reasons, a high speed pumping system, as well as a clean vacuum system, is now required. A newly developed electron microscope, the JEM-100CX features clean high vacuum in the vicinity of the specimen, realized by the use of a CASCADE type diffusion pump system which has been essentially improved over its predeces- sorD employed on the JEM-100C.

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