Tilting via torsion pairs and almost hereditary noetherian rings

We generalize the tilting process by Happel, Reiten and Smal{\o} to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi-tilted artin algebras as the almost hereditary ones to all right noetherian rings.Comment: 20 pages, v2: major revision, the title was changed, the paper was shortened, some results which had been found in the literature were remove

Second asymptomatic carotid surgery trial (ACST-2): a randomised comparison of carotid artery stenting versus carotid endarterectomy

Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence. Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362. Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86–1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91–1·32; p=0·21). Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable. Funding: UK Medical Research Council and Health Technology Assessment Programme

Wild tilted algebras revisited

In this paper wild tilted algebras are studied. Following [6] an algebra B is called tilted (of type A) if there exists a finite-dimensional hereditary algebra A over some field k and a tilting module T in the category A-mod of finite-dimensional left A-modules with B = EndA(T). The tilting module T has a structure as an (A,B)-bimodule and induces in B-mod a splitting torsion pair (X,Y), where the torsion-free class Y is the full subcategory of B-mod, defined by the objectsM with Tor1B(T,M) = 0, whereas the torsion class X is defined by the objects N with T ⊗B N = 0. A tilted algebra B of type A is only wild if A is wild hereditary. It was shown in [9] that the study of Y (respectively, X) can be reduced to the case of tilting modules without nonzero direct summands in the preinjective component I(A) (respectively, preprojective component P(A)). Only this case will be considered here, and it was shown in [9] that in this situation B is wild if and only if A is wild. In this paper the torsion-free class Y is studied, dual results hold for X. For basic terminology and general results we refer to [6, 16]. The main result of this paper is: Theorem 1. Let A be connected wild hereditary, T a tilting module in A-mod without indecomposable preinjective direct summand and B = EndA(T). If F = HomA(T,−) denotes the tilting functor and (Y,X) the torsion pair in B-mod induced by T, we have: 1. The Auslander–Reiten quiver Γ (B) of B has exactly one preprojective component P(B). (a) C = B/annP(B) is connected wild concealed. (b) If T0 is a preprojective direct summand of T, then F (T0) is pre-projective in B-mod. 2. If X ∈ Y is indecomposable and not in the connecting component, then: (a) τ−mB X is in C-mod for m 0

Message from Governor Otto Kerner, 1961

A letter from Governor Otto Kerner commending Chicago Kent College of Law upon the dedication of the remodeled building at 10 N. Franklin. Transcript:April 11, 1961 MESSAGE FROM GOVERNOR KERNER As Governor of Illinois, I am happy to send my greetings and best wishes to Chicago Kent College of Law on the occasion of dedication day for its newly remodeled building. I am certain I join with Chicago Kent\u27s more than 5,000 graduates, its many friends and benefactors in wishing the school faculty continued success in providing a major share of Chicago lawyers, members of our judiciary and leaders in state and city bar associations and civic organizations. We also commend Chicago Kent for selecting two outstanding representatives of the legal profession, Weymouth Kirkland, distinguished alumnus and member of the class of 1901 and Chief Justice Walter V. Schaefer, of the Illinois Supreme Court, as recipients of its first honorary degrees. We join with citizens throughout Illinois today to wish Chicago Kent College of Law a bright future as it continues to provide a legal education for mature, serious student of the law in its handsome quarters. Sincerely, Otto Kerner Governorhttps://scholarship.kentlaw.iit.edu/memorabilia/1008/thumbnail.jp