منابع مشابه
On Bernstein Algebras Which Are Train Algebras
holds in A. This class of algebras was introduced by Holgate [4], following the original work of Bernstein [2] and subsequent investigations by Lyubich [5] on idempotent quadratic maps from a real simplex into itself. A summary of known results on Bernstein algebras (up to 1980) is given in Worz-Busekros [8], which will also be used as a basic reference on algebras in genetics. All definitions ...
متن کاملOn Coalgebras which are Algebras
The category CoalgΣ of coalgebras with respect to a (bounded) signature Σ is known to be locally finitely presentable (see [1]). We strenghten this result by showing that CoalgΣ even is a presheaf category. Moreover, we give a presentation of this category as the category of all algebras of some (many-sorted) signature (without any equations). Σ–coalgebras, i.e., coalgebras with respect to a po...
متن کاملCluster-tilted Algebras Are Gorenstein and Stably Calabi-yau
We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...
متن کاملGorenstein Algebras Presented by Quadrics
We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different techniques, including liaison theory and generic initial ideals.
متن کاملDerived equivalences and Gorenstein algebras
In this note, we introduce the notion of Gorenstein algebras. Let R be a commutative Gorenstein ring and A a noetherian R-algebra. We call A a Gorenstein R-algebra if A has Gorenstein dimension zero as an R-module (see [2]), add(D(AA)) = PA, where D = HomR(−, R), and Ap is projective as an Rpmodule for all p ∈ Spec R with dim Rp < dim R. Note that if dim R = ∞ then a Gorenstein R-algebra A is p...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2019
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-018-09848-2